Layered Heusler alloys and methods for the fabrication and use thereof

ABSTRACT

Disclosed herein are layered Heusler alloys. The layered Heusler alloys can comprise a first layer comprising a first Heusler alloy with a face-centered cubic (fcc) crystal structure and a second layer comprising a second Heusler alloy with a fcc crystal structure, the second Heusler alloy being different than the first Heusler alloy, wherein the first layer and the second layer are layered along a layering direction, the layering direction being the [110] or [111] direction of the fcc crystal structure, thereby forming the layered Heusler alloy.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. Ser. No. 14/956,827, filedDec. 2, 2015, issued as U.S. Pat. No. 9,643,385 on May 9, 2017, which ishereby incorporated herein by reference in its entirety.

STATEMENT OF GOVERNMENT SUPPORT

This invention was made with government support under Grant No. 1235396awarded by the National Science Foundation and Agreement No.HR0011-13-3-0002 awarded by the Defense Advanced Research ProjectsAgency. The government has certain rights in this invention.

BACKGROUND

Memory and logic devices that utilize the electron's spin have elicitedinterest recently, in part because of scalability and power consumptionissues associated with more conventional electronic devices. Theperformance of many of these “spintronic” devices can be enhanced by theavailability of a material in the form of a thin film that combineshighly spin-polarized electron currents with magnetic anisotropyperpendicular to the plane of the film.

SUMMARY

Disclosed herein are layered Heusler alloys. The layered Heusler alloyscan comprise a first layer comprising a first Heusler alloy with aface-centered cubic (fcc) crystal structure and a second layercomprising a second Heusler alloy with a fcc crystal structure, thesecond Heusler alloy being different than the first Heusler alloy,wherein the first layer and the second layer are layered along alayering direction, the layering direction being the [110] or [111]direction of the fcc crystal structure, thereby forming the layeredHeusler alloy. In some examples, the layered Heusler alloy can furthercomprise a third layer comprising a third Heusler alloy with a fcccrystal structure, and the first layer, the second layer, and the thirdlayer are layered along the layering direction. The third Heusler alloycan be different than the first Heusler alloy and/or the second Heusleralloy.

In some examples, the first Heusler alloy can have a formula of A_(p)BC,wherein p is 1 or 2; A and B are each a transition metal, with theproviso that A and B are not the same transition metal; and C is anelement from Group 13, 14, or 15. In some examples, A and B are selectedfrom the group consisting of: scandium, titanium, vanadium, chromium,manganese, iron, cobalt, nickel, yttrium, zirconium, niobium,molybdenum, technetium, ruthenium, rhodium, and palladium. In someexamples, A and B are selected from the group consisting of: titanium,vanadium, chromium, manganese, iron, cobalt, nickel, rhodium, andpalladium. In some examples, C is selected from the group consisting of:boron, aluminum, gallium, indium, thallium, carbon, silicon, germanium,tin, lead, nitrogen, phosphorus, arsenic, antimony, and bismuth. In someexamples, C is selected from the group consisting of: aluminum, gallium,silicon, germanium, tin, phosphorus, arsenic, and antimony.

In some examples, the second Heusler alloy can have formula of X_(q)YZ,wherein q is 1 or 2; X and Y are each a transition metal, with theproviso that X and Y are not the same transition metal; and Z is anelement from Group 13, 14, or 15. In some examples, X and Y are selectedfrom the group consisting of: scandium, titanium, vanadium, chromium,manganese, iron, cobalt, nickel, yttrium, zirconium, niobium,molybdenum, technetium, ruthenium, rhodium, and palladium. In someexamples, X and Y are selected from the group consisting of: titanium,vanadium, chromium, manganese, iron, cobalt, nickel, rhodium, andpalladium. In some examples, Z is selected from the group consisting of:boron, aluminum, gallium, indium, thallium, carbon, silicon, germanium,tin, lead, nitrogen, phosphorus, arsenic, antimony, and bismuth. In someexamples, Z is selected from the group consisting of: aluminum, gallium,silicon, germanium, tin, phosphorus, arsenic, and antimony.

In some examples, the first Heusler alloy and the second Heusler alloycan be selected from the group consisting of Co₂CrSi, Co₂CrSb, Co₂FeAl,Co₂FeGe, Co₂FeSi, Co₂MnAl, Co₂MnGa, Co₂MnGe, Co₂MnSi, Co₂MnSb, Co₂TiGe,Co₂VGa, Co₂VSn, Cu₂MnAl, Cu₂MnIn, Cu₂MnSn, Cu₂MnBi, Fe₂MnAl, Fe₂MnGa,Fe₂MnSi, Fe₂TiGe, Fe₂TiSi, Fe₂VAl, Mn₂VGa, Ni₂MnAl, Ni₂MnIn, Ni₂MnGa,Pd₂MnAl, Pd₂MnIn, CoMnP, CoTiP, RhFeGe, RuMnAs, NiMnP, NiMnSi, andCoTiSi. In some examples, the first Heusler alloy and the second Heusleralloy can be selected from the group consisting of Co₂CrSi, Co₂CrSb,Co₂FeSi, Co₂MnAl, Co₂MnSi, Co₂MnSb, Co₂TiGe, Co₂VGa, Co₂VSn, Fe₂MnAl,Fe₂MnGa, Fe₂MnSi, Fe₂TiGe, Fe₂TiSi, CoMnP, CoTiP, RhFeGe, RuMnAs, NiMnP,NiMnSi, NiMnAs, NiMnSb, NiVSb, CoMnSb, and CoTiSi.

In some examples, the first Heusler alloy comprises a half metal or anear half metal. In some examples, the second Heusler alloy comprises ahalf metal or a near half metal. In some examples, the layered Heusleralloy comprises a half metal or a near half metal. In some examples, thelayered Heusler alloy has a Fermi level and a gapped spin-channel with agap, and wherein the Fermi level of the layered Heusler alloy fallswithin the gap of the gapped spin-channel of the layered Heusler alloy

In some examples, the layered Heusler alloy is layered along the [110]direction. In some examples, when the layered Heusler alloy is layeredalong the [110] direction, the first layer can a first number ofsublayers; the second layer can comprise a second number of sublayers;and the first number of sublayers is the same as the second number ofsublayers, such that the layered Heusler alloy has a unit cellcomprising (A_(p)BC)_(a)(X_(q)YZ)_(a), wherein a is the first number ofsublayers and a is an integer from 1 to 1000. In other embodiments, morethan 1000 layers can be present. The skilled artisan can use as manylayers as desired.

In some examples, the layered Heusler alloy is layered along the [111]direction. In some examples, when the layered Heusler alloy is layeredalong the [111] direction, the first layer comprises a first number ofsublayers, the first number of sublayers being 4, 6, or 8; the secondlayer comprises a second number of sublayers, the second number ofsublayers being 4, 6, or 8; and the sum of the first number of sublayersand second number of sublayers is 12. In some examples, when the firstnumber of sublayers is 4, the layered Heusler alloy has a unit cellcomprising (A_(p)BC)(X_(q)YZ)₂, wherein p and q are independently 1 or2. In some examples, when the first number of sublayers is 8, thelayered Heusler alloy has a unit cell comprising (A_(p)BC)₂(X_(q)YZ),wherein p and q are independently 1 or 2. In some examples, when thefirst number of sublayers is 6, the layered Heusler alloy has a unitcell comprising: (A_(p)BC)(A_(p-1)BZ)(X_(q)YZ), wherein p and q areindependently 1 or 2.

In some examples, the magnetocrystalline anisotropy of the layeredHeusler alloy along a direction perpendicular to the layering directioncan be from greater than 0 J/m³ to 10⁶ J/m³.

In some examples, the layered Heusler alloy has a μ₀H_(eff) of from −10to 10¹⁰ N A⁻¹ m⁻¹. In some examples, the magnetocrystalline anisotropyof the layered Heusler alloy is large enough to overcome ademagnetization field of a thin film. In some examples, the layeredHeusler alloy has a μ₀H_(eff) of greater than 0 N A⁻¹ m⁻¹.

In some examples, the layered Heusler alloys described herein can havehigh spin polarization at the Fermi energy, low damping, lowresistivity, high spin-torque efficiency, high tunnelingmagnetoresistance, or a combination thereof. In some examples, thelayered Heusler alloys described herein can be compatible with Heuslersemiconductors.

Methods of making and uses of the layered Heusler alloys are alsodescribed herein.

Additional advantages will be set forth in part in the description thatfollows, and in part will be obvious from the description, or may belearned by practice of the aspects described below. The advantagesdescribed below will be realized and attained by means of the elementsand combinations particularly pointed out in the appended claims. It isto be understood that both the foregoing general description and thefollowing detailed description are exemplary and explanatory only andare not restrictive.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1A displays the schematic crystal structure for a L2₁ full HeuslerA₂BC. The crystalline structure is cubic in nature (fcc).

FIG. 1B displays the schematic crystal structure for a C1_(b) halfHeusler ABC. The crystalline structure is cubic in nature (fcc).

FIG. 2 displays a schematic representation of stacking in the [001]direction for full Heusler superlattice A₂BC-X₂YZ. The [100] and [010]directions indicated in the figure correspond to those in the fcc cellin FIG. 1A.

FIG. 3 displays a schematic representation of stacking in [110]direction for a full Heusler superlattice A₂BC-X₂YZ. The [001] and [110]directions indicated in the figure corresponds to those in the fcc cellin FIG. 1A.

FIG. 4 displays a schematic representation of stacking in [111]direction for full Heusler superlattice A₂BC-X₂YZ. The [1 12] and [110]directions indicated in the figure are relative to axes defined for thefcc cell in FIG. 1A.

FIG. 5A displays the density of states for Co₂MnAl—Fe₂MnAl stacked in[001] direction with n=0.5 layering. This superlattice is a nearhalf-metal with gap width of 0.30 eV.

FIG. 5B displays the density of states for Co₂TiGe—Fe₂TiGe stacked in[001] direction with n=1.0 layering and gap width of 0.23 eV as ahalf-metal. The Fermi level is at 0 eV.

FIG. 6A displays the density of states for half-metallic Co₂MnSi—CoTiSisuperlattice stacked in [110] direction, n=1 with a band gap of 0.49 eV.

FIG. 6B displays the density of states for half-metallic CoMnP—CoTiPsuperlattice stacked in [111] direction with a big band gap of 1.35 eV.The Fermi level is at 0 eV.

FIG. 7A displays the density of states for a [001] stacked superlatticeof Co₂MnAl—Fe₂MnAl is doped with Si atoms at the Al atoms site. In cases(i) and (ii), Al and Si atoms are not mixed in a (001) plane. In cases(iii) and (iv), both Al and Si atoms can be there in a plane. When 50%of the Al are replaced with Si, the Fermi level moves 0.05 eV into theband gap, relative to the valence band edge.

FIG. 7B displays the density of states for a Co₂MnAl—Fe₂MnAlsuperlattice doped with Fe and Cr atoms at the Mn atom site. Doping withCr atoms move the Fermi level 0.05 eV into the band gap, but narrows thegap.

DETAILED DESCRIPTION

The compositions and methods described herein may be understood morereadily by reference to the following detailed description of specificaspects of the disclosed subject matter and the Examples and Figuresincluded therein.

Before the present compositions and methods are disclosed and described,it is to be understood that this disclosure is not limited to specificsynthetic methods or to particular reagents, as such may, of course,vary. It is also to be understood that the terminology used herein isfor the purpose of describing particular embodiments only and is notintended to be limiting.

Also, throughout this specification, various publications arereferenced. The disclosures of these publications in their entiretiesare hereby incorporated by reference into this application in order tomore fully describe the state of the art to which the disclosed matterpertains. The references disclosed are also individually andspecifically incorporated by reference herein for the material containedin them that is discussed in the sentence in which the reference isrelied upon.

General Definitions

The term “comprising” and variations thereof as used herein is usedsynonymously with the term “including” and variations thereof and areopen, non-limiting terms. Although the terms “comprising” and“including” have been used herein to describe various examples, theterms “consisting essentially of” and “consisting of” can be used inplace of “comprising” and “including” to provide for more specificexamples of the invention and are also disclosed. Other than in theexamples, or where otherwise noted, all numbers expressing quantities ofingredients, reaction conditions, and so forth used in the specificationand claims are to be understood at the very least, and not as an attemptto limit the application of the doctrine of equivalents to the scope ofthe claims, to be construed in light of the number of significant digitsand ordinary rounding approaches.

As used in the description and the appended claims, the singular forms“a,” “an,” and “the” include plural referents unless the context clearlydictates otherwise. Thus, for example, reference to “a composition”includes mixtures of two or more such compositions, reference to “anagent” includes mixtures of two or more such agents, reference to “thecomponent” includes mixtures of two or more such components, and thelike.

“Optional” or “optionally” means that the subsequently described eventor circumstance can or cannot occur, and that the description includesinstances where the event or circumstance occurs and instances where itdoes not.

It is understood that throughout this specification the identifiers“first”, “second” and “third” are used solely to aid in distinguishingthe various components and steps of the disclosed subject matter. Theidentifiers “first”, “second” and “third” are not intended to imply anyparticular order, amount, preference, or importance to the components orsteps modified by these terms.

Also, throughout this specification, various publications arereferenced. The disclosures of these publications in their entiretiesare hereby incorporated by reference into this application in order tomore fully describe the state of the art to which the disclosed matterpertains. The references disclosed are also individually andspecifically incorporated by reference herein for the material containedin them that is discussed in the sentence in which the reference isrelied upon.

Reference will now be made in detail to specific aspects of thedisclosed materials, compounds, compositions, articles, and methods,examples of which are illustrated in the accompanying examples andfigures.

Layered Heusler Alloys

Disclosed herein are layered Heusler alloys. The layered Heusler alloyscan comprise a first layer comprising a first Heusler alloy with aface-centered cubic (fcc) crystal structure and a second layercomprising a second Heusler alloy with a fcc crystal structure, thesecond Heusler alloy being different than the first Heusler alloy,wherein the first layer and the second layer are layered along alayering direction, the layering direction being the [110] or [111]direction of the fcc crystal structure, thereby forming the layeredHeusler alloy. As used herein, the layering direction being the [110] or[111] direction of the fcc crystal structure also includes thosedirections that are equivalent to the [110] or [111] direction of thefcc crystal due to symmetry of the fcc crystal. Directions equivalent tothe [110] or [111] directions of the fcc crystal structure due tosymmetry will be known to those of skill in the art. For example, in thefcc crystal structure, the [001], [010], [001], [010] and [100]directions are all equivalent by symmetry.

In some examples, the layered Heusler alloy can further comprise a thirdlayer comprising a third Heusler alloy with a fcc crystal structure, andthe first layer, the second layer, and the third layer are layered alongthe layering direction. The third Heusler alloy can be different thanthe first Heusler alloy and/or the second Heusler alloy.

The first Heusler alloy can comprise any full- or half-Heusler alloy. Insome examples, the first Heusler alloy can have a formula of A_(p)BC,wherein p is 1 or 2; A and B are each a transition metal, with theproviso that A and B are not the same transition metal; and C is anelement from Group 13, 14, or 15. When p is 2, the first Heusler alloyis a full-Heusler alloy with a L2₁ crystal structure and a unit cellformula of A₂BC, as shown in FIG. 1A. The L2₁ structure is fcc with a 4atom basis. When p is 1, the first Heusler alloy comprises ahalf-Heusler alloy with a C1_(b) crystal structure and a unit cellformula of ABC, as shown in FIG. 1B. The C1_(b) structure is fcc with a3 atom basis. The description of the layered Heusler alloys herein willbe based on the directions relative to the fcc cells, for example asshown in FIGS. 1A and 1B.

In some examples, A and B are selected from the group consisting of:scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel,yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, rhodium,and palladium. In some examples, A and B are selected from the groupconsisting of: titanium, vanadium, chromium, manganese, iron, cobalt,nickel, rhodium, and palladium.

In some examples, C is selected from the group consisting of: boron,aluminum, gallium, indium, thallium, carbon, silicon, germanium, tin,lead, nitrogen, phosphorus, arsenic, antimony, and bismuth. In someexamples, C is selected from the group consisting of: aluminum, gallium,silicon, germanium, tin, phosphorus, arsenic, and antimony.

The second Heusler alloy can comprise any full- or half-Heusler alloy.In some examples, the second Heusler alloy can have formula of X_(q)YZ,wherein q is 1 or 2; X and Y are each a transition metal, with theproviso that X and Y are not the same transition metal; and Z is anelement from Group 13, 14, or 15. When q is 1, the second Heusler alloyis a half-Heusler alloy with a C1_(b) crystal structure and a unit cellof XYZ. When q is 2, the second Heusler alloy is a full-Heusler alloywith a L2₁ crystal structure.

In some examples, X and Y are selected from the group consisting of:scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel,yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, rhodium,and palladium. In some examples, X and Y are selected from the groupconsisting of: titanium, vanadium, chromium, manganese, iron, cobalt,nickel, rhodium, and palladium.

In some examples, Z is selected from the group consisting of: boron,aluminum, gallium, indium, thallium, carbon, silicon, germanium, tin,lead, nitrogen, phosphorus, arsenic, antimony, and bismuth. In someexamples, Z is selected from the group consisting of: aluminum, gallium,germanium, tin, phosphorus, arsenic, and antimony.

The first Heusler alloy and the second Heusler alloy are different. Insome examples, when the first Heusler alloy is A_(p)BC and the secondHeusler alloy is X_(q)YZ, A and X are not the same transition metal. Insome examples, when the first Heusler alloy is A_(p)BC and the secondHeusler alloy is X_(q)YZ, B and Y are not the same transition metal. Insome examples, when the first Heusler alloy is A_(p)BC and the secondHeusler alloy is X_(q)YZ, C and Z are not the same element from Group13, 14, or 15.

In some examples, the first Heusler alloy and the second Heusler alloycan be selected from the group consisting of Co₂CrSi, Co₂CrSb, Co₂FeAl,Co₂FeGe, Co₂FeSi, Co₂MnAl, Co₂MnGa, Co₂MnGe, Co₂MnSi, Co₂MnSb, Co₂TiGe,Co₂VGa, Co₂VSn, Cu₂MnAl, Cu₂MnIn, Cu₂MnSn, Cu₂MnBi, Fe₂MnAl, Fe₂MnGa,Fe₂MnSi, Fe₂TiGe, Fe₂TiSi, Fe₂VAl, Mn₂VGa, Ni₂MnAl, Ni₂MnIn, Ni₂MnGa,Pd₂MnAl, Pd₂MnIn, CoMnP, CoTiP, RhFeGe, RuMnAs, NiMnP, NiMnSi, andCoTiSi. In some examples, the first Heusler alloy and the second Heusleralloy can be selected from the group consisting of Co₂CrSi, Co₂CrSb,Co₂FeSi, Co₂MnAl, Co₂MnSi, Co₂MnSb, Co₂TiGe, Co₂VGa, Co₂VSn, Fe₂MnAl,Fe₂MnGa, Fe₂MnSi, Fe₂TiGe, Fe₂TiSi, CoMnP, CoTiP, RhFeGe, RuMnAs, NiMnP,NiMnSi, NiMnAs, NiMnSb, NiVSb, CoMnSb, and CoTiSi.

In some examples, the first Heusler alloy comprises a half metal or anear half metal. As used herein, a Heusler alloy is a “half-metal” whenthe Fermi energy falls in a gap for one of the spin-channels, but notfor the other. A “near half metal,” on the other hand, occurs when theFermi energy falls slightly outside the gap for one of the spin channels(Munira K et al. J. Appl. Phys. 2014, 115, 17B731). In some examples,the second Heusler alloy comprises a half metal or a near half metal. Insome examples, the layered Heusler alloy comprises a half metal or anear half metal. In some examples, the layered Heusler alloy has a Fermilevel and a gapped spin-channel with a gap, and wherein the Fermi levelof the layered Heusler alloy falls within the gap of the gappedspin-channel of the layered Heusler alloy

The highest Fermi-energy spin-polarization comes from ferromagneticmaterials that exhibit half-metallic properties. In half-metals, theelectronic structure of one of the spin channels is that of a metalwhile the other is that of an insulator or semiconductor (Munira K etal. J. Appl. Phys. 2014, 115, 17B731). In some examples, this can leadto 100% spin-polarization of the electron current, highmagnetoresistance and high spin-torque efficiency. Half-metals can alsohave lower magnetic damping than typical ferromagnets (Liu C et al. J.Appl. Phys. 2009, 95, 2). Low damping can be beneficial for applicationsthat utilize Spin-Torque transfer for switching of nanomagnets (Munira Ket al. IEEE Transactions on Electron Devices. 2012, 59, 8).

In some examples, the layered Heusler alloy is layered along the [110]direction. In some examples, when the layered Heusler alloy is layeredalong the [110] direction, the first layer can a first number ofsublayers; the second layer can comprise a second number of sublayers;and the first number of sublayers is the same as the second number ofsublayers, such that the layered Heusler alloy has a unit cellcomprising (A_(p)BC)_(a)(X_(q)YZ)_(a), wherein a is the first number ofsublayers and a is an integer from 1 to 1000. In some examples, therecan be more than 1000 sublayers. In some examples, a is 1, 2, or 3.

When the layered Heusler alloy is formed by stacking layers along the[110] direction, each layer is stoichiometric. Referring now to FIG. 3,a schematic for a first Heusler alloy comprising A₂BC and a secondHeusler alloy comprising X₂YZ being layered along the [110] direction,with the first layer and second layer each having one sublayer is shown.As shown in FIG. 3, atoms A, B and C are each present in the first(sub)layer and X, Y, and Z atoms are each present in the second(sub)layer. The unit cell in FIG. 3 corresponds to the first layer andsecond layer each having one sublayer, for which one layer of eachconstituent alternates one after another ( . . . -A₂BC-X₂YZ- . . . ).For two and three sublayers, the thickness of each layer of the layeredHeusler alloy is increased by 2 ( . . . -A₂BC-A₂BC-X₂YZ-X₂YZ- . . . )and 3 times ( . . . -A₂BC-A₂BC-A₂BC-X₂YZ-X₂YZ-X₂YZ- . . . ),respectively.

If the first Heusler alloy and the second Heusler alloy were each ahalf-Heusler, one of the A atoms in the A₂BC layer and one of the Xatoms in the X₂YZ layer of FIG. 3 would be replaced by a vacancy. Thelayered Heusler alloy formed from two half-Heuslers (e.g., the firstHeusler alloy being ABC and the second Heusler alloy being XYZ) with 1,2 and 3 sublayers corresponds to ( . . . -ABC-XYZ- . . . ), ( . . .-ABC-ABC-XYZ-XYZ- . . . ) and ( . . . -ABC-ABC-ABC-XYZ-XYZ-XYZ- . . . ),respectively.

In some examples, when the layered Heusler alloy is layered along the[110] direction, the first Heusler alloy is A_(p)BC, and the secondHeusler alloy is X_(q)YZ, A and X are not the same transition metal. Insome examples, when the layered Heusler alloy is layered along the [110]direction, the first Heusler alloy is A_(p)BC, and the second Heusleralloy is X_(q)YZ, B and Y are not the same transition metal and C and Zare not the same element from Group 13, 14, or 15.

In some examples, the layered Heusler alloy is layered along the [111]direction. In some examples, when the layered Heusler alloy is layeredalong the [111] direction, the first layer comprises a first number ofsublayers, the first number of sublayers being 4, 6, or 8; the secondlayer comprises a second number of sublayers, the second number ofsublayers being 4, 6, or 8; and the sum of the first number of sublayersand second number of sublayers is 12. In some examples, when the firstnumber of sublayers is 4, the layered Heusler alloy has a unit cellcomprising (A_(p)BC)(X_(q)YZ)₂, wherein p and q are independently 1 or2. In some examples, when the first number of sublayers is 8, thelayered Heusler alloy has a unit cell comprising (A_(p)BC)₂(X_(q)YZ),wherein p and q are independently 1 or 2. In some examples, when thefirst number of sublayers is 6, the layered Heusler alloy has a unitcell comprising: (A_(p)BC)(A_(p-1)XBZ)(X₁YZ), when p and q areindependently 1 or 2.

When the layered Heusler alloy is formed by stacking layers along the[111] direction, the layering can comprise the stacking of hexagonalnets, as can be seen from the depiction of layers perpendicular to the[111] direction shown in FIG. 4. The fcc cells shown in FIGS. 1A and 1Bare also helpful in understanding [111] layering. The fcc lattice with asingle atom basis can be viewed along the [111] direction as asuccession of identical hexagonal layers with A-B-C stacking. The L2₁structure is fcc but with a 4 atom basis. There is a single species oneach layer. For full-Heuslers, for example with an X₂YZ composition, theatomic layers perpendicular to the [111] direction follow the pattern ofY species on A, followed by X species on B, then Z species on C, X on A,Y on B, etc. In some examples, when the layered Heusler alloy is formedby stacking layers along the [111] direction, the correct stoichiometryfor a full-Heusler (e.g., the first Heusler is A₂BC and the secondHeusler is X₂YZ) requires a minimum of 4 sublayers for each of the firstHeusler alloy and the second Heusler alloy (e.g., at least 4 sublayersin each of the first layer and the second layer), and the total numberof repeating sublayers must be divisible by three to make the A-B-Csequence repeat. Thus for the case wherein the first Heusler alloy isA₂BC and the second Heusler alloy is X₂YZ, a minimum of 12 sublayers isrequired for the simulation of a Heusler superlattice stacked in thismanner. As shown in FIG. 4, there may be six layers of A₂BC and then sixlayers of X₂YZ. One can also have 8 layers of A₂BC followed by 4 layersof X₂YZ or vice versa. Half-Heuslers do not contain any atoms in thesecond, sixth and tenth layers in the schematic structure of FIG. 4.

Due to the spin-orbit interaction and the symmetry of the crystal, themagnetic moments of a material will want to point in a particulardirection in an infinite or spherical crystal. Meanwhile, layeredsystems can have a special direction perpendicular to the layers. Thedifference in the energy per unit volume of the layered material whenthe moments are pointed perpendicular to the layers compared to theminimum energy when they point in the plane of the layers is themagnetocrystalline anisotropy, K (sometimes with a subscript “u”,K_(u)). In other words, the magnetocrystalline anisotropy (K, sometimeswith a subscript “u”, K_(u)) of a layered Heusler alloy can becalculated by using the energy differences,E_(in-plane)−E_(perpendicular), where E_(perpendicular) represents theenergy when magnetization orientation is perpendicular to the stackingplanes and E_(in-plane) is the energy when magnetization orientation isalong any direction in the stacking plane. For example, for layeredHeusler alloys layered in the [110] direction, the energy calculated forthe [110] magnetization can be compared to that calculated for thein-plane magnetization directions [001], [110], and [111]. For layeredHeusler alloys layered in the [111] direction, for example, the energycalculated for the [111] magnetization can be compared to thatcalculated for the in-plane magnetization directions [1 12] and [110]. Apositive value for the magnetocrystalline anisotropy (e.g., K>0) canindicate that the magnetization prefers to lie perpendicular to theHeusler planes, while a negative value indicates that the magnetizationlies in-plane.

There is a different kind of anisotropy called shape anisotropy that canbe important for a thin film. For a thin film, the moments want to liehead to tail (south adjacent to north), just like many small magnets,and they can best do this when they lie in-plane.

In some examples, the layered Heusler alloy can have amagnetocrystalline anisotropy of greater than 0 J/m³ along a directionperpendicular to the layering direction (e.g., 1 J/m³ or more, 2 J/m³ ormore, 3 J/m³ or more, 4 J/m³ or more, 5 J/m³ or more, 6 J/m³ or more, 7J/m³ or more, 8 J/m³ or more, 9 J/m³ or more, 10 J/m³ or more, 20 J/m³or more, 30 J/m³ or more, 40 J/m³ or more, 50 J/m³ or more, 60 J/m³ ormore, 70 J/m³ or more, 80 J/m³ or more, 90 J/m³ or more, 1×10² J/m³ ormore, 2×10² J/m³ or more, 3×10² J/m³ or more, 4×10² J/m³ or more, 5×10²J/m³ or more, 6×10² J/m³ or more, 7×10² J/m³ or more, 8×10² J/m³ ormore, 9×10² J/m³ or more, 1×10³ J/m³ or more, 2×10³ J/m³ or more, 3×10³J/m³ or more, 4×10³ J/m³ or more, 5×10³ J/m³ or more, 6×10³ J/m³ ormore, 7×10³ J/m³ or more, 8×10³ J/m³ or more, 9×10³ J/m³ or more, 1×10⁴J/m³ or more, 2×10⁴ J/m³ or more, 3×10⁴ J/m³ or more, 4×10⁴ J/m³ ormore, 5×10⁴ J/m³ or more, 6×10⁴ J/m³ or more, 7×10⁴ J/m³ or more, 8×10⁴J/m³ or more, 9×10⁴ J/m³ or more, 1×10⁵ J/m³ or more, 2×10⁵ J/m³ ormore, 3×10⁵ J/m³ or more, 4×10⁵ J/m³ or more, 5×10⁵ J/m³ or more, 6×10⁵J/m³ or more, 7×10⁵ J/m³ or more, 8×10⁵ J/m³ or more, or 9×10⁵ J/m³ ormore).

In some examples, the magnetocrystalline anisotropy of the layeredHeusler alloy along a direction perpendicular to the layering directioncan be 10⁶ J/m³ or less (e.g., 9×10⁵ J/m³ or less, 8×10⁵ J/m³ or less,7×10⁵ J/m³ or less, 6×10⁵ J/m³ or less, 5×10⁵ J/m³ or less, 4×10⁵ J/m³or less, 3×10⁵ J/m³ or less, 2×10⁵ J/m³ or less, 1×10⁵ J/m³ or less,9×10⁴ J/m³ or less, 8×10⁴ J/m³ or less, 7×10⁴ J/m³ or less, 6×10⁴ J/m³or less, 5×10⁴ J/m³ or less, 4×10⁴ J/m³ or less, 3×10⁴ J/m³ or less,2×10⁴ J/m³ or less, 1×10⁴ J/m³ or less, 9×10³ J/m³ or less, 8×10³ J/m³or less, 7×10³ J/m³ or less, 6×10³ J/m³ or less, 5×10³ J/m³ or less,4×10³ J/m³ or less, 3×10³ J/m³ or less, 2×10³ J/m³ or less, 1×10³ J/m³or less, 9×10² J/m³ or less, 8×10² J/m³ or less, 7×10² J/m³ or less,6×10² J/m³ or less, 5×10² J/m³ or less, 4×10² J/m³ or less, 3×10² J/m³or less, 2×10² J/m³ or less, 1×10² J/m³ or less, 90 J/m³ or less, 80J/m³ or less, 70 J/m³ or less, 60 J/m³ or less, 50 J/m³ or less, 40 J/m³or less, 30 J/m³ or less, 20 J/m³ or less, 10 J/m³ or less, 9 J/m³ orless, 8 J/m³ or less, 7 J/m³ or less, 6 J/m³ or less, 5 J/m³ or less, 4J/m³ or less, 3 J/m³ or less, 2 J/m³ or less, or 1 J/m³ or less).

The magnetocrystalline anisotropy of the layered Heusler alloy along adirection perpendicular to the layering direction can range from any ofthe minimum values described above to any of the maximum valuesdescribed above. For example, the magnetocrystalline anisotropy of thelayered Heusler alloy along a direction perpendicular to the layeringdirection can be from greater than 0 J/m³ to 10⁶ J/m³ (e.g., fromgreater than 0 J/m³ to 1×10³ J/m³, from 1×10³ J/m³ to 10⁶ J/m³, from 0J/m³ to 1×10² J/m³, from 1×10² J/m³ to 1×10⁴ J/m³, from 1×10⁴ J/m³ to10⁶ J/m³, or from 10 J/m³ to 9×10⁵ J/m³).

The effective anisotropy field of a thin magnetic film, H_(eff) (or,μ₀H_(eff) where μ₀ is the magnetic permeability constant), can bedescribed by:

${\mu_{0}H_{eff}} = \frac{{2K} - M_{s}^{2}}{M_{s}}$where μ₀ is the magnetic permeability constant, K is themagnetocrystalline anisotropy, and M_(s) is the saturation magnetizationof the magnetic film due to magnetic dipole interactions. Accordingly, athin magnetic film with no magnetocrystalline anisotropy (K=0) will havean effective anisotropy field of μ₀H_(eff)=−M_(s). A positive value ofμ₀H_(eff) can indicate that the Heusler superlattice has enoughperpendicular anisotropy to overcome the demagnetization field of a thinfilm.

In some examples, the layered Heusler alloy can have a μ₀H_(eff) of −10N A⁻¹ m⁻¹ or more (e.g., −5 N A⁻¹ m⁻¹ or more, 0 N A⁻¹ m⁻¹ or more, 5 NA⁻¹ m⁻¹ or more, 10 N A⁻¹ m⁻¹ or more, 20 N A⁻¹ m⁻¹ or more, 30 N A⁻¹m⁻¹ or more, 40 N A⁻¹ m⁻¹ or more, 50 N A⁻¹ m⁻¹ or more, 60 N A⁻¹ m⁻¹ ormore, 70 N A⁻¹ m⁻¹ or more, 80 N A⁻¹ m⁻¹ or more, 90 N A⁻¹ m⁻¹ or more,1×10² N A⁻¹ m⁻¹ or more, 2×10² N A⁻¹ m⁻¹ or more, 3×10² N A⁻¹ m⁻¹ ormore, 4×10² N A⁻¹ m⁻¹ or more, 5×10² N A⁻¹ m⁻¹ or more, 6×10² N A⁻¹ m⁻¹or more, 7×10² N A⁻¹ m⁻¹ or more, 8×10² N A⁻¹ m⁻¹ or more, 9×10² N A⁻¹m⁻¹ or more, 1×10³ N A⁻¹ m⁻¹ or more, 2.5×10³ N A⁻¹ m⁻¹ or more, 5×10³ NA⁻¹ m⁻¹ or more, 7.5×10³ N A⁻¹ m⁻¹ or more, 1×10⁴ N A⁻¹ m⁻¹ or more,2.5×10⁴ N A⁻¹ m⁻¹ or more, 5×10⁴ N A⁻¹ m⁻¹ or more, 7.5×10⁴ N A⁻¹ m⁻¹ ormore, 1×10⁵ N A⁻¹ m⁻¹ or more, 2.5×10⁵ N A⁻¹ m⁻¹ or more, 5×10⁵ N A⁻¹m⁻¹ or more, 7.5×10⁵ N A⁻¹ m⁻¹ or more, 1×10⁶ N A⁻¹ m⁻¹ or more, 2.5×10⁶N A⁻¹ m⁻¹ or more, 5×10⁶ N A⁻¹ m⁻¹ or more, 7.5×10⁶ N A⁻¹ m⁻¹ or more,1×10⁷ N A⁻¹ m⁻¹ or more, 2.5×10⁷ N A⁻¹ m⁻¹ or more, 5×10⁷ N A⁻¹ m⁻¹ ormore, 7.5×10⁷ N A⁻¹ m⁻¹ or more, 1×10⁸ N A⁻¹ m⁻¹ or more, 2.5×10⁸ N A⁻¹m⁻¹ or more, 5×10⁸ N A⁻¹ m⁻¹ or more, 7.5×10⁸ N A⁻¹ m⁻¹ or more, 1×10⁹ NA⁻¹ m⁻¹ or more, 2.5×10⁹ N A⁻¹ m⁻¹ or more, 5×10⁹ N A⁻¹ m⁻¹ or more, or7.5×10⁹ N A⁻¹ m⁻¹ or more).

In some examples, the layered Heusler alloy can have a μ₀H_(eff) of 10¹⁰N A⁻¹ m⁻¹ or less (e.g., 7.5×10⁹ N A⁻¹ m⁻¹ or less, 5×10⁹ N A⁻¹ m⁻¹ orless, 2.5×10⁹ N A⁻¹ m⁻¹ or less, 1×10⁹ N A⁻¹ m⁻¹ or less, 7.5×10⁸ N A⁻¹m⁻¹ or less, 5×10⁸ N A⁻¹ m⁻¹ or less, 2.5×10⁸ N A⁻¹ m⁻¹ or less, 1×10⁸ NA⁻¹ m⁻¹ or less, 7.5×10⁷ N A⁻¹ m⁻¹ or less, 5×10⁷ N A⁻¹ m⁻¹ or less,2.5×10⁷ N A⁻¹ m⁻¹ or less, 1×10⁷ N A⁻¹ m⁻¹ or less, 7.5×10⁶ N A⁻¹ m⁻¹ orless, 5×10⁶ N A⁻¹ m⁻¹ or less, 2.5×10⁶ N A⁻¹ m⁻¹ or less, 1×10⁶ N A⁻¹m⁻¹ or less, 7.5×10⁵ N A⁻¹ m⁻¹ or less, 5×10⁵ N A⁻¹ m⁻¹ or less, 2.5×10⁵N A⁻¹ m⁻¹ or less, 1×10⁵ N A⁻¹ m⁻¹ or less, 7.5×10⁴ N A⁻¹ m⁻¹ or less,5×10⁴ N A⁻¹ m⁻¹ or less, 2.5×10⁴ N A⁻¹ m⁻¹ or less, 1×10⁴ N A⁻¹ m⁻¹ orless, 7.5×10³ N A⁻¹ m⁻¹ or less, 5×10³ N A⁻¹ m⁻¹ or less, 2.5×10³ N A⁻¹m⁻¹ or less, 1×10³ N A⁻¹ m⁻¹ or less, 7.5×10² N A⁻¹ m⁻¹ or less, 5×10² NA⁻¹ m⁻¹ or less, 2.5×10² N A⁻¹ m⁻¹ or less, 1×10² N A⁻¹ m⁻¹ or less, 90N A⁻¹ m⁻¹ or less, 80 N A⁻¹ m⁻¹ or less, 70 N A⁻¹ m⁻¹ or less, 60 N A⁻¹m⁻¹ or less, 50 N A⁻¹ m⁻¹ or less, 40 N A⁻¹ m⁻¹ or less, 30 N A⁻¹ m⁻¹ orless, 20 N A⁻¹ m⁻¹ or less, 10 N A⁻¹ m⁻¹ or less, 5 N A⁻¹ m⁻¹ or less, 0N A⁻¹ m⁻¹ or less, or −5 N A⁻¹ m⁻¹ or less).

In some examples, the layered Heusler alloy has a μ₀H_(eff) of from −10to 10¹⁰ N A⁻¹ m⁻¹ (e.g., from −10 N A⁻¹ m⁻¹ to 1×10⁵ N A⁻¹ m⁻¹, from1×10⁵ N A⁻¹ m⁻¹ to 1×10¹⁰ N A⁻¹ m⁻¹, from −10 N A⁻¹ m⁻¹ to 1×10² N A⁻¹m⁻¹, from 1×10² N A⁻¹ m⁻¹ to 1×10⁴ N A⁻¹ m⁻¹, from 1×10⁴ N A⁻¹ m⁻¹ to1×10⁶ N A⁻¹ m⁻¹, from 1×10⁶ N A⁻¹ m⁻¹ to 1×10⁸ N A⁻¹ m⁻¹, from 1×10⁸ NA⁻¹ m⁻¹ to 1×10¹⁰ N A⁻¹ m⁻¹, or from 0 N A⁻¹ m⁻¹ to 1×10¹⁰ N A⁻¹ m⁻¹).In some examples, the magnetocrystalline anisotropy of the layeredHeusler alloy is large enough to overcome a demagnetization field of athin film. In some examples, the layered Heusler alloy has a μ₀H_(eff)of greater than 0 N A⁻¹ m⁻¹.

In some examples, the layered Heusler alloys described herein can havehigh spin polarization at the Fermi energy, low damping, lowresistivity, high spin-torque efficiency, high tunnelingmagnetoresistance, or a combination thereof. In some examples, thelayered Heusler alloys described herein can be compatible with Heuslersemiconductors.

Methods of Making

The layered Heusler alloys described herein can be made, for example, bythin film processing techniques, such as sputtering, pulsed layerdeposition, molecular beam epitaxy, evaporation, atomic layerdeposition, or combinations thereof. In some examples, the layeredHeusler alloys described herein can be made, for example, usingequilibrium processing methods, such as arc melting, annealing, orcombinations thereof.

Methods of Use

The layered Heusler alloys described herein can be used, for example, inspintronic devices, spin logic devices, spin valves, magnetic tunneljunctions, or a combination thereof.

In some examples, the layered Heusler alloys described herein can beused in Magnetoresistive random-access memory devices. Magnetoresistiverandom-access memory (MRAM) is a non-volatile random access-memorytechnology that uses magnetic storage elements to store data, unlike theelectric charge or current flows used to store data in conventional RAMchip technologies.

In some examples, the layered Heusler alloys described herein can beused in spin-torque transfer devices, such as spin-transfer,torque-based logic devices that use spins and magnets for informationprocessing. Spin-torque transfer is an effect in which the orientationof a magnetic layer can be modified using a spin-polarized current.Spin-torque transfer can be used to flip the active elements in magneticrandom-access memory. Spin-torque transfer magnetic random-access memory(e.g., STT-RAM or STT-MRAM) has the advantages of lower powerconsumption and better scalability over conventional magnetoresistiverandom-access memory (MRAM) which uses magnetic fields to flip theactive elements. Spin-torque transfer technology can combine lowercurrent requirements and reduced cost in making MRAM devices. In someexamples, the layered Heusler alloys described herein can form the freelayer in a STT-RAM device. In some examples, the layered Heusler alloysdescribed herein can form the reference (or pinned) layer in a STT-RAMdevice. In some examples, the layered Heusler alloys described hereincan be used to form an all-Heusler magnetic tunnel junction, for exampleby layering a semiconducting Heusler alloy with a half-metallic Heusleralloy.

In some examples, the layered Heusler alloys can be used as theferromagnetic free layer in spin memory devices.

EXAMPLES

The following examples are set forth below to illustrate the methods andresults according to the disclosed subject matter. These examples arenot intended to be inclusive of all aspects of the subject matterdisclosed herein, but rather to illustrate representative methods andresults. These examples are not intended to exclude equivalents andvariations of the present invention which are apparent to one skilled inthe art.

Efforts have been made to ensure accuracy with respect to numbers (e.g.,amounts, temperature, etc.) but some errors and deviations should beaccounted for. Unless indicated otherwise, parts are parts by weight,temperature is in ° C. or is at ambient temperature, and pressure is ator near atmospheric. There are numerous variations and combinations ofreaction conditions, e.g., component concentrations, temperatures,pressures and other reaction ranges and conditions that can be used tooptimize the product purity and yield obtained from the describedprocess. Only reasonable and routine experimentation will be required tooptimize such process conditions.

Example 1

Certain full-Heusler alloys (Skaftouros S et al. Phys. Rev. B. 2013, 87,024420; Galanakis I et al. J. Phys. D: Appl. Phys. 2006, 39, 765) andhalf-Heusler alloys (Galanakis I et al. Phys. Rev. B. 2008, 77, 214417;Kandpal H C et al. J. Phys. D: Appl. Phys. 2006, 39, 5) have been shown(e.g., by calculation) to be half-metals or “near” half-metals. Ahalf-metal occurs when the Fermi energy falls in a gap for one of thespin-channels, but not for the other. Thus electron transport at theFermi energy (if spin-flip scattering and spin mixing effects areignored) is metallic for the channel without a gap and activated for thegapped channel. The gap in the full- and half-Heusler alloys can occursuch that the number of filled bands below the gap is three times thenumber of atoms per formula unit (i.e. for an average of three electronsper atom). Full and half-Heusler alloys can have a gap at three bandsper atom. A “near half metal,” on the other hand, occurs when the Fermienergy falls slightly outside the gap for one of the spin channels(Munira K et al. J. Appl. Phys. 2014, 115, 17B731).

One drawback of Heusler alloys, for some applications, is that thesymmetry of their L2₁ and C1_(b) crystal structures can precludeuniaxial magnetocrystalline anisotropy. A uniaxial symmetry can beinduced by a surface or an interface, for example when a thin layer ofHeusler alloy has an interface with MgO (Munira K et al. J. Appl. Phys.2014, 115, 17B731; Wen Z et al. Appl. Phys. Lett. 2011, 98, 242507) orGaAs (Wang W H et al. Phys. Rev. B. 2005, 71, 144416). However, such aninduced magnetocrystalline anisotropy is proportional to the area of theinterface rather than the volume of the alloy. If this interfacialanisotropy is perpendicular, it will eventually be counterbalanced bythe demagnetization anisotropy as the thickness of the Heusler alloy isincreased. One possible exception would be a ferrimagnetic Heusler alloywith zero net magnetic moment.

Herein, ab-initio simulations demonstrate that an intrinsic uniaxialanisotropy can be achieved by making layered superlattices of twoHeusler alloys. Various full-full, full-half and half-half Heuslersuperlattices are studied and potential half-metallic superlattices withperpendicular magnetocrystalline anisotropy are identified. Thisuniaxial anisotropy in the superlattice can be caused by the differentelectronic configurations of the two Heusler alloys and/or by thedistortion of the lattice, which can cause the local environment of eachatom to be different in the direction perpendicular to the layers fromthat in the plane of the layers.

Previous theoretical calculations have shown that it is possible forhalf-metallic Heusler superlattices comprising multiple Heusler alloyslayered perpendicular to the [001] direction to retain theirhalf-metallicity (Culbert C A et al. J. Appl. Phys. 2008, 103, 07D707;Tirpanci S et al. J. Appl. Phys. 2013, 113, 043912; Liu C et al.arXiv:1103.3855, 2011). Herein, the possibility of Heusler alloyslayered perpendicular to the [110] and [111] directions retaininghalf-metallicity is investigated. In addition, the effects of symmetryreduction due to said layering is investigated, particularly withrespect to magnetocrystalline anisotropy. The identification of Heuslersuperlattices that are half-metallic and also have sufficientperpendicular magnetic anisotropy to off-set the demagnetization fieldof a thin ferromagnetic layer that might occur, for example, in theferromagnetic layers of an Spin-Torque Transfer Random Access Memory(STT-RAM) device (Apalkov D et al. J. Emerg. Technol. Comput. Syst.2013, 9, 2), is discussed herein.

Layering in the [001] Direction

In bulk full-Heusler alloys, A₂ and BC planes are stacked alternatelyalong the [001] direction. For half-Heuslers, A and BC planes alternate.For both alloy types, four of these atomic layers stacked along the[001] direction are needed to complete a supercell with the correctsymmetry for all atoms. FIG. 2 illustrates the unit cell of asuperlattice with layers stacked along the [001] direction and composedof two full-Heusler alloys, A₂BC and X₂YZ. This unit cell corresponds ton=0.5 layering (in the terminology of Tirpanci S et al. J. Appl. Phys.2013, 113, 043912), for which layers of each Heusler alloy alternate oneafter another, with each Heusler alloy having two layers. In otherwords, the unit cell for the Heusler superlattice comprising twofull-Heusler alloys, namely A₂BC and X₂YZ, would comprise a first layerpopulated by A atoms, followed by a second layer populated by B and Catoms, a third layer populated by X atoms, and a fourth layer populatedby Y and Z atoms. Thus, an n=0.5 superlattice comprising twofull-Heusler alloys can be described by . . . -A₂-BC-X₂-ZY- . . . where“ZY” (rather than “YZ”) indicates that the positions of the transitionand non-transition metal have been interchanged between the second andfourth layers. As used herein, this stacking is also referred to as “twolayer stacking,” indicating there are two atomic layers per Heusleralloy in the super lattice. For half-Heusler superlattices, the secondand fourth layers are the same, but one of the two atomic sites inlayers 1 and 3 that would have been occupied by an A or X atom in thefull-Heusler is vacant, with the positions of the atom and vacancyalternating between layers 1 and 3.

Two layer stacking is called n=0.5 because the representation of a purefull-Heusler with cubic symmetry requires a supercell with 4 atomic[001] layers. When the number of layers for each constituent alloy isdoubled (e.g., four layer stacking), the resulting superlattice will besaid have n=1.0 layers (e.g., . . . -A₂-BC-A₂-CB-X₂-YZ-X₂-ZY- . . . ).Similarly, n=1.5 corresponds to 6 layers each of A₂BC and X₂YZ ( . . .-A₂-BC-A₂-CB-A₂-BC-X₂-ZY-X₂-YX-X₂-ZY- . . . ).

Layering in the [110] Direction

When the superlattice is formed by stacking layers along the [110]direction, each layer is stoichiometric. As shown in FIG. 3, A, B and Catoms are present in each layer. The unit cell in FIG. 3 corresponds ton=0.5 layering of a full-Heusler alloy, for which one layer of eachconstituent alternates one after another ( . . . -A₂BC-X₂YZ- . . . ).For n=1 and n=1.5, the thickness of each constituent of the superlatticeis increased by 2 ( . . . -A₂BC-A₂BC-X₂YZ-X₂YZ- . . . ) and 3 times ( .. . -A₂BC-A₂BC-A₂BC-X₂YZ-X₂YZ-X₂YZ- . . . ), respectively.

For a half-Heusler, one of the A atoms in the A₂BC layer and one of theX atoms in the X₂YZ layer would be replaced by a vacancy. For thehalf-Heusler superlattice, n=0.5, 1.0 and 1.5 layering corresponds to (. . . -ABC-XYZ- . . . ), ( . . . -ABC-ABC-XYZ-XYZ- . . . ) and ( . . .-ABC-ABC-ABC-XYZ-XYZ-XYZ- . . . ), respectively. Symmetry does not allowperpendicular magnetic anisotropy for Heusler superlattices stacked inthe [110] direction for n=0.5 if A=X or if B=Y and C=Z, because, in suchcases, the superlattice is geometrically equivalent in the [110] and[110] directions. Systems with this degeneracy are omitted from Table 3.

As described in more detail below, the results of the investigationsdiscussed herein indicate that (110) textured Heuslers and half-Heuslerscan retain their half-metallicity. In this context “textured” means thatthe film is growing in such a manner that the atomic planes parallel tothe plane of the film are perpendicular to the [110] direction. This maybe useful in growing textured Heusler films. A full-Heusler alloy withrandom site occupation would be bcc. Alloys with bcc structure oftenprefer [110] growth because the atomic planes tend to be most dense forthis growth direction. Denser planes that are further apart can lead toa lower surface energy. Herein, values of the formation energy per atomfor the different layering directions and layer thicknesses werecalculated in lieu of calculating surface energies.

Layering in the [111] Direction

Layering in the [111] direction comprises the stacking of hexagonalnets, as can be seen from the depiction of layers perpendicular to the[111] direction shown in FIG. 4. The fcc cells shown in FIGS. 1A and 1Bare also helpful in understanding [111] layering. The fcc lattice with asingle atom basis can be viewed along the [111] direction as asuccession of identical hexagonal layers with the familiar A-B-Cstacking. The L2₁ structure is fcc but with a 4 atom basis. There is asingle species on each layer. For full-Heuslers with an X₂YZcomposition, the atomic layers perpendicular to the [111] directionfollow the pattern of Y species on A, followed by X species on B, then Zspecies on C, X on A, Y on B, etc. The correct stoichiometry for afull-Heusler requires a minimum of 4 layers for each type of Heusler andthe total number of repeating layers must be divisible by three to makethe A-B-C sequence repeat. Thus for the case A₂BC-X₂YZ, a minimum of 12layers is required for the simulation of a Heusler superlattice stackedin this manner. As shown in FIG. 4, there may be six layers of A₂BC andthen six layers of X₂YZ. One can also have 8 layers of A₂BC followed by4 layers of X₂YZ or vice versa. Half-Heuslers do not contain any atomsin the second, sixth and tenth layers in the schematic structure of FIG.4.

Computational Approach

Calculations were performed using the Vienna Ab-Initio SimulationPackage (VASP) (Kresse G and Hafner J. Phys. Rev. B. 1993, 47, 558;Kresse G and Furthmüller J. Phys. Rev. B. 1996, 54, 11169) with thePerdew-Burke-Ernzerhof formulation of the generalized gradientapproximation (GGA) (Wang Y and Perdew J P. Phys. Rev. B. 1991, 44,13298) for the exchange-correlation potential. The superlattices wererelaxed without any constraint on shape or volume, using theconjugate-gradient algorithm. A high kinetic energy cutoff of 520electron volts (eV) was used during unit cell relaxation in order toguarantee accuracy and ensure that the calculated atomic forces areconsistent with the energy(i.e., to ensure that the forces vanish at theenergy minimum). The Brillouin zone sampling was performed according tothe Monkhorst-Pack scheme. The Kohn-Sham equations were solved to findthe charge distribution of the ground state system without takingspin-orbit interactions into account. Finally, the total energy of thesystem was calculated for a given orientation of magnetic moments in thepresence of spin-orbit coupling.

Due to the spin-orbit interaction and the symmetry of the crystal, themagnetic moments of a material will want to point in a particulardirection in an infinite or spherical crystal. Meanwhile, layeredsystems can have a special direction perpendicular to the layers. Thedifference in the energy per unit volume of the layered material whenthe moments are pointed perpendicular to the layers compared to theminimum energy when they point in the plane of the layers is themagnetocrystalline anisotropy, K (sometimes with a subscript “u”,K_(u)). In other words, the magnetic anisotropy of a superlattice (K,sometimes with a subscript “u”, K_(u)) is calculated by using the energydifferences, E_(in-plane)−E_(perpendicular). E_(perpendicular)represents the energy when magnetization orientation is perpendicular tothe stacking planes. E_(in-plane) is the energy when magnetizationorientation is along any direction in the stacking plane.

For [001]-stacked superlattices, the energy calculated for the [001]magnetization direction was compared to that calculated for the [110]and [100] directions. For superlattices stacked in the [110] direction,the energy calculated for the [110] magnetization was compared to thatcalculated for the in-plane magnetization directions [001], [110], and[111]. For superlattices stacked in the [111] direction, the energycalculated for the [111] magnetization was compared to that calculatedfor the in-plane magnetization directions [1 12] and [110]. A positivevalue for K indicates that the magnetization prefers to lieperpendicular to the Heusler planes, while a negative value indicatesthat the magnetization lies in-plane.

The formation energy per atom for the layered superlattice wascalculated by subtracting the energies of the individual elements inpure form from the superlattice's total energy. For a layered n=0.5A₂BC-X₂YZ superlattice, the formation energy per atom (E_(form)) is:

$E_{form} = \frac{( {E_{{A_{2}{BC}} - {X_{2}{YZ}}} - {2E_{A}} - E_{B} - E_{C} - {2E_{X}} - E_{Y} - E_{Z}} )}{8}$

where E_(A) ₂ _(BC-X) ₂ _(YZ) is the total energy of the superlatticeunit cell containing 8 atoms (two A, one B, one C, two X, one Y and oneZ), and E_(A), E_(B), E_(C), E_(X), E_(Y), and E_(Z) stand for theenergies when each of the A, B, C, X, Y and Z elements crystallize inpure metals, respectively. If the formation energy per atom is positive,the superlattice is unstable and cannot be formed in equilibriumconditions. A negative formation energy per atom suggests that such asuperlattice film can be grown. However, a negative formation energydoes not, for example, guarantee against formation of binary or ternaryphases comprising any two or three of the available six elements.

Results and Discussion

For this study, sixteen Heusler superlattices were simulated forlayering perpendicular to the [001] and [110] directions and eight weresimulated for layering perpendicular to the [111] direction. The 16superlattices for the layered Heuslers are composed of 14 distinct fullHeuslers and 7 distinct half-Heusler alloys. The bulk properties ofthese Heusler alloys are listed in Table 1. Individual Heusler alloyswhich are already experimentally realized are noted with a † sign. Thealloys that have citations but no † signs are those for whichtheoretical predictions are available in the art, but not experimentalconfirmation. Compounds without citations are alloys that were found tohave a negative formation energy herein, but for which no otherexperimental or theoretical reports were available.

The 21 Heusler alloys listed in Table 1 have gaps in the minority spinchannel density of electronic states at 3 electrons per atom. This gapis referred to herein as the Slater-Pauling gap because Slater andPauling noted in the 1930s that certain bcc-based alloys tend tomaintain approximately three electrons per atom in the minorityspin-channel. Table 1 also gives the calculated width of this gap. Forsome of the alloys, the Fermi energy is in (or is calculated to be in)this gap, generating a half-metal (e.g., Co₂MnSi, NiMnP) which aredenoted by (HM) in the column of Table 1 that lists the width of thegap.

For three of the alloys listed in Table 1, namely Fe₂TiSi, Fe₂TiGe, andCoTiP, there is an average of 6 valence electrons per atom, such that itis possible to have a Slater-Pauling gap in both spin channels. Theresults of the calculations discussed herein indicated that theseHeusler alloys have identical gaps in both channels. These alloys aredenoted by (SC) adjacent to the gap width values in Table 1.

For CoTiSi, the Fermi energy is not in the gap, but is within 0.03 eV offalling in the gap. Herein, alloys whose Fermi energy falls outside thegap but within an energy distance from the gap of 0.05 eV are referredto as “near half-metals” and denoted by (NHM) in the column with the gapwidth values in Table 1. For five of the alloys in Table I, the Fermienergy falls outside of the gap and is further than 0.05 eV from thegap. Even though these alloys are not predicted to be half-metals ornear half-metals as bulk alloys, they can be used in certain layeredsystems to make near half-metal or half-metal superlattices.

The column in Table 1 labeled “Distance from E_(F) to gap” gives thedistance (in eV) from the Fermi energy to the gap edge. Thus, for thehalf-metals, it gives the distance to the nearest band edge and thenotation in parentheses indicates whether the nearest band edge is theconduction band (CB) or the valence band (VB). For some applications ofhalf-metals, it can be desirable to have the Fermi energy as far from aband edge as possible. For the alloys that are not predicted to behalf-metals, the number in the “Distance from E_(F) to gap” column givesthe energy difference between the Fermi energy and the closest bandedge, and the notation in parentheses tells whether the Fermi energyfalls below (VB) or above (CB) the gap. For some applications it mightbe desirable for this energy distance to be small, e.g. to make iteasier to use alloying or electrochemical potentials to move the Fermienergy into the gap.

TABLE 1 Lattice constants, magnetic moments, formation energies, andcalculated energy gaps of 14 full-Heusler and 7 half-Heusler alloys.Magnetic Distance Lattice moment Formation Gap from EF constant per unitenergy per Width* to gap Heusler a (Å) cell (μB) atom (eV) (eV) (eV)Curie temperature (K) Co₂MnAl† 5.71 4.009 −0.349 0.477 0.149 950(Sakuraba Y et al. Appl. Phys. Lett. 2006, 88, 022503) (VB) (Kim K etal. Physica Status Solidi B. 2004, 241, 7) Fe₂MnAl† 5.67 2.002 −0.1830.376 0.0886 400 (Ando Y et al Spintronics. ed Felser C and Fecher GH.(VB) (Vinesh A et al. J. Appl. Phys. Springer Netherlands, 2013, p.355-366) 2009, 105, 07A309) Fe₂MnGa† 5.69 2.0145 −0.067 0.083 0.2374 750(Kudryavtsev YV et al. Acta Materialia 2012, 60, 12; (VB) (Gasi T et al.J Appl. Phys. Gasi T et al. J. Appl. Phys. 2013, 113, 17E301) 2013, 113,17E301) CO₂MnSi† 5.63 5 −0.433 0.669 0.310 985 (Picozzi S et al. Phys.Rev. B. 2004, 69, 094423; (HM) (VB) (Sakuraba Y et al. Appl. Phys.Kammerer S et al. Appl. Phys. Lett. 2004, 85, 79) Lett. 2006, 88,192508) Fe₂MnSi 5.56 3 −0.332 0.405 0.067 215 (Mori H et al. Thin SolidFilms. 2012, 520, 15; Hamad B (VB) (Brown PJ et al. J. Magnetism and andHu Q. Physica Status Solidi (b). 2011, 248, 12) Magnetic Mater. 1985,50, 2) CO₂FeSi† 5.66 5.4642 −0.349 0.040 0.628 1100 (Kandpal HC et al.Phys. Rev. B. 2006, 73, 094422; (CB) (Wurmehl S et al. Phys. Rev B.Inomata K et al. J. Phys. D: Appl. Phys. 2006, 39, 816) 2005, 72,184434) Fe₂TiSi† 5.69 0 −0.666 0.32 — — (Meinert M et al. Phys. Rev. B.2014, 90, 085127) (SC) Co₂VGa† 5.76 2 −0.277 0.14 0.025 369 (Han H etal. J. Phys. D: Appl. Phys. 2012, 111, 9; (HM) (CB) (Kubler J et al.Phys. Rev. B. Kanomata T et al. Phys. Rev. B. 2010, 82, 144415) 2007,76, 024414) Co₂VSn 6.07 3 −0.041 0.376 0.093 103 (Mahmoud NT et al.Intermetallics. 2013, 33, 0) (HM) (CB) (Kubler J et al. Phys. Rev. B.2007, 76, 024414) CO₂TiGe† 5.84 2 −0.470 0.425 0.0813 380 (Prathiba G etal. J. Magnetism and Magnetic Mater. (HM) (CB) (Barth J et al. Phil.Trans. R. 2011, 323, 1) Soc. A. 2011, 369, 3588) Fe₂TiGe 5.78 0 −0.4520.1 — — (Luo H et al. J. Magnetism and Magnetic Mater. (SC) 2012, 324,20) Co₂MnSb 6.02 6 −0.069 0.486 0.063 600 (Huang HM et al. Physica B:Condensed Matter. (HM) (CB) (Manea AS et al. J. Crystal 2011, 406, 8)Growth. 2005, 205, 1) Co₂CrSb 6.01 5 0.066 0.385 0.088 — (Kanbur U andGokoglu G. J. Magnetism and Magnetic (HM) (CB) Mater. 2011, 323, 9)CO₂CrSi 5.66 4 −0.305 0.682 0.3336 747 (Rai DP et al. Bull. Mater. Sci.2011, 34, 6) (HM) (VB) (Chen XW et al. J. Appl. Phys. 2006, 100, 113901)CoMnP 5.34 3 −0.325 1.1 0.493 583 (Fujii S et al. J. Phys. F: MetalPhys. 1988, 18, 5) (HM) (CB) (Fruchart R et al. J. Appl. Phys. 1969, 40,1250) CoTiP 5.43 0 −0.988 1.37 — — (SC) RhFeGe 5.77 3 −0.128 0.46 0.077— (HM) (CB) RuMnAs 5.76 2 −0.032 0.78 0.012 — (Antonov VN et al. Phys.Rev. B. 1997, 56, 20) (HM) (VB) NiMnSi 5.43 3 −0.139 0.87 0.325 715(Galanakis I et al. J. Appl. Phys. 2008, 104, 083916) (HM) (VB) (Dinh VAet al. J. Phys. Soc. Jpn. 2008, 77, 014705) NiMnP 5.46 4 −0.193 0.890.302 1050 (Singh M et al. AIP Conf. Proceed.. 2011, 1393, 1) (HM) (CB)(Dinh VA et al. J. Phys. Soc. Jpn. 2008, 77, 014705) CoTiSi 5.58 0.998−0.561 1.16 0.0291 — (Kawaharada Y et al. J. Alloys and Compounds. (NHM)(VB) 2004, 384, 1) *In column “Gap Width”: NHM indicates a nearlyhalf-metallic alloy with Fermi level within 0.05 eV of the bandgap. HMindicates a half-metallic superlattice with the Fermi level inside theband gap. SC indicates that the material is predicted to be asemiconductor with a Slater-Pauling gap in both spin-channels.

The results of calculations of the properties of certain layered Heusleralloys for layering in the [001], [110], and [111] directions are listedin Tables 2, 3, and 4, respectively. Generally, the Slater-Pauling gapswere found to be robust. The size of the gap in the multi-layer and itsposition relative to the Fermi energy varies with the direction oflayering and with the thickness of the layers. In general, the resultsindicated the gap width for the layered Heusler will be between those ofthe individual Heuslers that comprise the layered Heusler system.Similarly, the results indicated that layering half-metals generallyyields half-metallic multilayers.

One exception to these general trends is the layered systemCo₂TiGe—Fe₂TiGe [001] n=0.5. The parent alloys are a Slater-Paulinghalf-metal (CO₂TiGe) and a Slater-Pauling semiconductor (Fe₂TiGe),respectively. The results of the calculations indicated the layeredstructure was a half-metal for [001] n=1.0 and n=1.5 layering, but notfor n=0.5. This can be due to the nature of the semiconductor Fe₂TiGe,which is predicted to be a non-magnetic semiconductor despite being 50%Fe. The energy reduction achieved by making a Slater-Paulingsemiconductor can be sufficient to “kill” the magnetic moment of Fe.Other Heuslers which show this effect are Fe₂VAl and Fe₂TiSi. Theresults discussed herein suggest that it is more difficult, however, tokill the Fe moment when the Fe atoms have second neighbors that are Co,for example as occurs in Co₂TiGe—Fe₂TiGe [001] n=0.5, when the layersare extremely thin.

The results discussed herein indicate that layering of gapped Heuslersthat are not half-metals or near-half-metals can, in some examples, movethe Fermi energy closer to the gap or even into the gap. One example isa layered Heusler structure comprising Co₂MnAl and Fe₂MnAl. Both of theparent alloys have Slater-Pauling gaps, but the Fermi energy falls atleast 0.88 eV below the gap edge for both parent alloys. However, all ofthe layered Co₂MnAl—Fe₂MnAl systems investigated herein had a Fermienergy closer to the gap edge than either of the parent alloys.

One strategy for moving the Fermi energy into the gap can be layering aHeusler that has its Fermi energy in the valence band with anotherHeusler that has its Fermi energy in the conduction band. An example ofthis is layering Co₂MnAl with Co₂FeSi. The latter has a tiny gap that isfar from the Fermi energy in DFT calculations, although it can be madeinto a half-metal by application of a sufficiently large U in a LDA+Ucalculation (Balke B et al. Phys. Rev. B. 2006, 74, 104405). However,Co₂MnAl—Co₂FeSi can yield half-metals when layered in the [001], [110],or [111] directions.

Table 2 lists the geometric and magnetic properties of superlatticesystems layered along the [001] direction for three different values ofthe constituent thicknesses as labeled by n. Since the x- andy-directions perpendicular to the layering direction, (z), areequivalent, these superlattices will have tetragonal symmetry afterrelaxation. For these systems, both the in-plane lattice constant, “a”,and a ratio labeled “c/a” that indicates the degree of tetragonaldistortion of the lattice, are reported. The c/a number is actuallyC/(2na), where C is the length of the supercell in the [001] direction.A value of c/a of 1.0000 indicates no tetragonal distortion. For most ofthe systems herein, this distortion was small.

The magnetocrystalline anisotropy (K) is calculated by taking thedifference between the energy when magnetization is aligned in the [001]direction and the lowest energy in-plane. The direction of themagnetization when the energy is the lowest in-plane is indicated in themagnetocrystalline anisotropy column (K) in Table 2.

The effective anisotropy field of a thin magnetic film, H_(eff) (or,μ₀H_(eff) where μ₀ is the magnetic permeability constant), can bedescribed by:

${\mu_{0}H_{eff}} = \frac{{2K} - M_{s}^{2}}{M_{s}}$where μ₀ is the magnetic permeability constant, K is themagnetocrystalline anisotropy, and M_(s) is the saturation magnetizationof the magnetic film due to magnetic dipole interactions. Accordingly, athin magnetic film with no magnetocrystalline anisotropy (K=0) will havean effective anisotropy field of μ₀H_(eff)=−M_(s). Even if K is greaterthan 0, μ₀H_(eff) can be negative. A negative value of μ₀H_(eff)indicates that the magnetic dipole interactions of the thin film arestrong enough to pull the magnetic moment directions into the plane ofthe film. Conversely, a positive value of μ₀H_(eff), for example asshown in Table 2, can indicate that the Heusler superlattice has enoughperpendicular anisotropy to overcome the demagnetization field of a thinfilm.

TABLE 2 Lattice constants, c/a, magnetic moments and formation energiesof various Heusler superlattices layered in [001] direction for threedifferent thicknesses, n. Magnetic Lattice moment Formation Distanceconstant per unit K × 10⁵ energy per μ₀H_(eff) Gap Width from E_(f) toSuperlattice n a (Å) c/a cell (μ_(B)) (J/m³) atom (eV) (N A⁻¹m⁻¹) (eV)gap (eV) Co₂MnAl—Fe₂MnAl 0.5 5.70 0.9993 6.000   6.807 [110] −0.263 1.500.30 (NHM) 0.015 (VB) 1.0 5.68 1.0024 12.015 −0.687 [110] −0.264 −0.990.37 0.072 (VB) 1.5 5.70 0.9973 18.039   1.253 [110] −0.266 −0.35 0.310.087 (VB) Co₂MnAl—Co₂FeSi 0.5 5.70 0.9921 10.000 −1.646 [100] −0.405−1.60 0.19 (HM) 0.019 (CB) 1.0 5.69 0.9935 20.000   0.105 [110] −0.392−1.26 0.23 (HM) 0.067 (CB) 1.5 5.73 0.9849 29.772 −2.765 [110] −0.366−1.82 0.01 0.165 (CB) Co₂MnAl—Fe₂MnGa 0.5 5.72 0.9964 6.013   7.175[110] −0.205 1.64 0.11 0.124 (VB) 0.5 5.72 1.0000 6.014   7.365 [110]−0.203 1.72 0.08 0.120 (VB) 1.0 5.70 1.0020 12.086   1.275 [110] −0.208−0.34 0.10 0.169 (VB) 1.5 5.71 0.9966 18.164   1.099 [110] −0.210 −0.390.06 0.181 (VB) Co₂MnSi—Fe₂MnSi 0.5 5.57 1.0056 8.013 −2.940 [110]−0.379 −1.76 0.33 0.065 (VB) 1.0 5.57 1.0053 16.001 −2.631 [100] −0.379−1.46 0.51 (HM) 0.095 (VB) 1.5 5.57 1.0077 24.000 −0.324 [110] −0.380−1.15 0.47 (HM) 0.108 (VB) Co₂MnSi—Co₂FeSi 0.5 5.60 1.0072 10.979 −2.134[110] −0.397 −1.82 0.14 0.388 (CB) 1.0 5.60 1.0033 21.598 −1.027 [110]−0.394 −1.61 0.28 0.244 (CB) 1.5 5.61 1.0054 31.994 −1.009 [110] −0.390−1.59 0.08 0.429 (CB) Co₂MnSi—Fe₂TiSi 0.5 5.78 0.9688 5.000 −0.280 [100]−0.543 −0.75 0.36 (HM) 0.152 (VB) 1.0 5.69 0.9915 10.000   0.118 [110]−0.550 −0.60 0.42 (HM) 0.172 (CB) 1.5 5.67 0.9968 15.000 −0.989 [100]−0.557 −1.03 0.41 (HM) 0.194 (CB) Co₂VGa—Co₂VSn 0.5 5.94 0.9875 5.000  0.520 [110] −0.211 −0.34 0.26 (HM) 0.028 (CB) 1.0 5.90 0.9963 9.999  1.164 [100] −0.180 −0.06 0.31 (HM) 0.072 (CB) 1.5 6.00 0.9688 15.000  4.668 [100] −0.157 1.47 0.23 (HM) 0.012 (CB) Co₂TiGe—Fe₂TiGe 0.5 5.721.0216 0.620   0.643 [110] −0.446 2.11 No gap — 1.0 5.86 0.9868 4.000  3.421 [100] −0.460 3.39 0.23 (HM) 0.057 (CB) 1.5 5.81 0.9725 5.996  2.246 [100] −0.430 1.99 0.14 (HM) 0.020 (CB) Co₂MnSb—Co₂CrSb 0.5 6.040.9938 11.000   0.721 [110] −0.019 −1.02 0.43 (HM) 0.116 (CB) 1.0 6.020.9981 22.000 −0.109 [110] −0.017 −1.20 0.43 (HM) 0.083 (CB) 1.5 6.020.9987 33.000 −0.032 [110] −0.016 −1.18 0.43 (HM) 0.084 (CB)Co₂CrSi—Fe₂MnAl 0.5 5.79 0.9637 6.000 −0.641 [110] −0.298 −0.98 0.42(HM) 0.112 (VB) 1.0 5.68 0.9912 12.000 −1.864 [110] −0.268 −1.38 0.38(HM) 0.076 (VB) 1.5 5.67 0.9956 18.000 −1.647 [100] −0.261 −1.31 0.37(HM) 0.063 (VB) Co₂CrSi—Fe₂MnGa 0.5 5.82 0.9581 6.000 −2.199 [110]−0.237 −1.49 0.33 (NHM) 0.018 (VB) 1.0 5.71 0.9879 12.000 −3.157 [110]−0.210 −1.80 0.27 (NHM) 0.037 (VB) 1.5 5.68 0.9937 18.012 −2.833 [100]−0.203 −1.69 0.23 0.062 (VB) Co₂CrSi—Fe₂MnSi 0.5 5.69 0.9781 7.000  0.074 [100] −0.333 −0.90 0.48 (HM) 0.136 (VB) 1.0 5.69 0.9772 14.000−0.427 [110] −0.329 −1.04 0.48 (HM) 0.111 (VB) 1.5 5.67 0.9823 21.000−0.097 [100] −0.327 −0.95 0.45 (HM) 0.094 (VB) CoMnP—CoTiP 0.5 5.391.0049 3.000   3.106 [110] −0.740 1.33 1.32 (HM) 0.594 (CB) 1.0 5.401.0012 6.000 −1.326 [110] −0.754 −1.19 1.32 (HM) 0.595 (CB) 1.5 5.401.0025 9.000 −1.333 [110] −0.761 −1.20 1.33 (HM) 0.604 (CB)RhFeGe—RuMnAs 0.5 5.79 1.0002 5.136 −2.281 [110] −0.088 −1.55 0.18 0.173(VB) 1.0 5.78 1.0025 10.000 −2.537 [100] −0.095 −1.66 0.48 (NHM) 0.016(VB) 1.5 5.77 1.0041 14.998 −0.280 [100] −0.096 −0.72 0.41 (HM) 0.023(VB) NiMnSi—NiMnP 0.5 5.47 0.9959 7.000   0.303 [100] −0.345 −0.93 0.84(HM) 0.409 (VB) 1.0 5.47 0.9981 14.000 −0.369 [100] −0.343 −1.09 0.82(HM) 0.404 (CB) 1.5 5.46 1.0005 21.000   0.496 [110] −0.340 −0.88 0.77(HM) 0.369 (CB) Co₂MnSi—CoTiSi 0.5 5.63 0.9867 4.015 −7.817 [110] −0.509−4.19 0.04 0.136 (VB) 0.5 5.63 1.0000 4.081 −1.692 [100] −0.468 −1.33 Nogap — 1.0 5.62 0.9897 8.067 −3.945 [110] −0.537 −2.37 0.26 0.082 (VB)1.5 5.61 0.9935 12.267 −1.366 [110] −0.528 −1.17 0.17 0.135 (VB)

In Table 3, the analogous properties for layering along the [110]direction are presented. A [110] layered Heusler alloy can berepresented by a supercell with 2 atomic layers. Thus for [110]layering, n=0.5 would represent alternating layers A₂BC-X₂YZ.

For a [110]-layered superlattice with n=0.5, the [110] (in-plane)direction can be geometrically equivalent to the [110] (perpendicular)direction in certain cases, i.e. for A=X, or for B=Y and C=Z. Thus, forthese cases, perpendicular magnetocrystalline anisotropy can only beobtained for layer thicknesses of n=1 or greater. As such, n=0.5layering for [110] was not calculated herein for these cases.

For [110] layering, both c/a and c/b are reported. Both of these columnshave been adjusted so that layering of two Heusler alloys with identicallattice constants and no distortions would yield c/a=c/b=1.0000. Thus,the reported c/a is actually cV/(na) and c/b is actually 2C/(nb), whereC is the dimension of the superlattice in the direction of layering.

The results discussed herein indicate that the gaps are generallyslightly larger for [110] layering than for [001] layering. Furthermore,when the Fermi energy falls outside the gap, the [110] layered systemstend to have the Fermi energy closer to the gap than the corresponding[001] layered systems.

Layering in the [110] direction offers the opportunity for magneticanisotropy in the plane of the layers as well as for a differencebetween the energy between the in-plane and perpendicular directions.The direction for which the lowest energy was found is indicated inTable 3.

TABLE 3 Summary of the geometric and magnetic properties of variousHeusler superlattices for three different thicknesses n, layering in[110] direction. Magnetic Formation Lattice moment energy per Distanceconstant per unit K × 10⁵ atom μ₀H_(eff) Gap Width from E_(f) toSuperlattice n a (Å) c/a c/b cell (μ_(B)) (J/m³) (eV) (N A⁻¹m⁻¹) (eV)gap (eV) Co₂MnAl—Fe₂MnAl 1.0 5.71 0.9955 1.0012 12.001   1.654 [001]−0.262 −0.21 0.40 (NHM) 0.046 (VB) 1.5 5.71 0.9941 1.0013 18.000   1.350[001] −0.258 −0.31 0.37 (NHM) 0.011 (VB) Co₂MnAl—Co₂FeSi 1.0 5.66 1.00070.9989 20.000 −2.201 [110] −0.398 −1.71 0.33 (HM) 0.153 (CB) 1.5 5.661.0007 0.9989 29.999 −3.029 [110] −0.389 −1.87 0.22 (HM) 0.013 (CB)Co₂MnAl—Fe₂MnGa 0.5 5.73 0.9921 0.9916 6.004 −0.199 [110] −0.191 −0.820.16 0.074 (VB) 1.0 5.73 0.9948 1.0013 12.057   1.540 [001] −0.204 −0.250.22 0.164 (VB) 1.5 5.73 0.9947 1.0013 18.045   1.159 [001] −0.201 −0.370.21 0.116 (VB) Co2MnSi—Fe₂MnSi 1.0 5.57 1.0079 0.9990 16.000 −7.431[110] −0.385 −2.82 0.58 (HM) 0.066 (VB) 1.5 5.56 1.0117 0.9994 24.000−4.901 [110] −0.387 −2.22 0.59 (HM) 0.108 (VB) Co2MnSi—Co₂FeSi 1.0 5.631.0009 1.0001 21.778 −0.497 [110] −0.405 −1.50 0.34 0.204 (CB) 1.5 5.631.0005 1.0001 32.357 −0.092 [111] −0.403 −1.42 0.24 0.299 (CB)Co₂MnSi—Fe₂TiSi 0.5 5.66 1.0056 0.9958 5.000 −1.193 [001] −0.530 −1.110.36 (HM) 0.135 (VB) 1.0 5.64 1.0059 1.0026 10.000 −0.096 [110] −0.543−0.68 0.50 (HM) 0.194 (VB) 1.5 5.65 1.0038 1.0022 15.000 −0.289 [110]−0.552 −0.76 0.47 (HM) 0.193 (VB) Co₂VGa—Co₂VSn 1.0 5.89 0.9983 1.002010.000   0.001 [001] −0.210 −0.57 0.30 (HM) 0.041 (CB) 1.5 5.91 0.99631.0010 15.000 −0.285 [001] −0.209 −0.63 0.28 (HM) 0.045 (CB)Co₂TiGe—Fe₂TiGe 1.0 5.77 1.0107 0.9976 4.000 −0.909 [110] −0.459 −1.200.26 (HM) 0.064 (VB) 1.5 5.79 1.0046 0.9974 6.000   0.455 [110] −0.4600.24 0.24 (HM) 0.095 (CB) Co₂MnSb—Co₂CrSb 1.0 6.02 0.9981 0.9997 21.998  1.149 [001] −0.019 −0.93 0.43 (HM) 0.092 (CB) 1.5 6.01 0.9998 0.999633.000 −0.308 [001] −0.017 −1.24 0.43 (HM) 0.079 (CB) Co₂CrSi—Fe₂MnAl0.5 5.62 0.9979 1.0131 6.000 −0.857 [001] −0.282 −1.05 0.48 (HM) 0.083(VB) 1.0 5.68 0.9939 0.9884 11.999 −3.021 [001] −0.275 −1.75 0.45 (HM)0.054 (VB) 1.5 5.63 1.0048 0.9988 18.000 −1.254 [001] −0.269 −1.18 0.41(HM) 0.097 (VB) Co₂CrSi—Fe₂MnGa 0.5 5.65 0.9930 1.0071 6.000 −1.852[001] −0.216 −0.77 0.31 (NHM) 0.048 (VB) 1.0 5.68 0.9892 0.9883 12.000−3.615 [001] −0.214 −1.95 0.32 (NHM) 0.035 (VB) 1.5 5.64 1.0036 0.998518.000 −1.800 [001] −0.208 −1.36 0.26 (NHM) 0.015 (VB) Co₂CrSi—Fe₂MnSi0.5 5.55 1.0087 1.0209 7.000 −0.840 [001] −0.330 −1.15 0.51 (HM) 0.134(VB) 1.0 5.58 1.0059 0.9971 14.000 −1.653 [001] −0.325 −1.37 0.56 (HM)0.140 (VB) 1.5 5.54 1.0191 1.0016 21.000 −2.409 [001] −0.326 −1.58 0.59(HM) 0.140 (VB) CoMnP—CoTiP 1.0 5.41 0.9997 0.9980 6.000 −0.188 [001]−0.747 −0.55 1.35 (HM) 0.561 (CB) 1.5 5.41 0.9976 0.9985 9.000   0.360[001] −0.720 −0.24 1.32 (HM) 0.624 (CB) RhFeGe—RuMnAs 0.5 5.76 1.00851.0054 5.069 −5.910 [110] −0.093 −3.05 0.17 0.265 (VB) 1.0 5.77 0.99990.9949 10.000   3.820 [111] −0.100 0.99 0.47 (NHM) 0.012 (VB) 1.5 5.781.0016 1.0011 15.001 −2.234 [110] −0.099 −1.53 0.43 (NHM) 0.037 (VB)NiMnSi—NiMnP 1.0 5.45 1.0024 0.9983 14.000   0.409 [111] −0.348 −0.900.83 (HM) 0.407 (CB) 1.5 5.45 1.0010 0.9980 21.000   0.026 [001] −0.232−0.99 0.81 (HM) 0.380 (VB) Co₂MnSi—CoTiSi 0.5 5.64 0.9846 0.9867 4.015  7.817 [001] −0.509 3.11 0.04 0.136 (VB) 1.0 5.59 0.9921 0.9965 8.000  2.699 [001] −0.553 0.72 0.49 (HM) 0.125 (VB) 1.5 5.59 0.9968 0.998112.000   2.418 [001] −0.552 0.59 0.47 (HM) 0.083 (VB)

Table 4 presents results for layering along the [111] direction foreight Heusler pairs for the minimal 12 layer geometry required torepresent the full-Heusler alloy geometry. For [111] layering, eachatomic layer is a relatively sparsely populated hexagonal net containingonly a single species. The column labeled “Lattice constant” gives thein-plane nearest neighbor distance a multiplied by √{square root over(2)}, which would correspond to the Heusler lattice constant for thepure Heusler system. The column labeled c/a lists the c-axis of thesupercell divided by √{square root over (6)}a, where a is the in-planenearest neighbor distance. This ratio would be 1.000 for the cubicHeusler lattice. A value in this column greater than unity indicatesthat the lattice is stretched in [111] direction relative to thein-plane direction.

Three types of stacking within this twelve layer supercell wereinvestigated: 8-4, meaning 8 layers of Heusler 1 followed by 4 layers ofHeusler 2; 4-8, meaning 4 layers of Heusler 1 followed by 8 layers ofHeusler 2; and 6-6, meaning 6 layers of Heusler 1 followed by 6 layersof Heusler 2.

TABLE 4 Summary of the geometric and magnetic properties of variousHeusler superlattice, stacked in [111] direction. Heusler A₂BC isfollowed by layers of Heusler X₂YZ. For half-Heuslers, O represents avacant layer. Magnetic Lattice moment Formation Distance constant perunit K × 10⁵ Energy per μ₀H_(eff) Gap Width from E_(f) to SuperlatticeStacking order a (Å) c/a cell (μB) (J/m³) atom (eV) (N A⁻¹m⁻¹) (eV) gap(eV) Co₂MnSi—Fe₂MnSi BACABACAYXZX 5.61 1.0035 13.000 −3.924 [112] −0.404−2.01 0.62 (HM) 0.084 (VB) BACABAZXYXZX 5.61 1.0022 12.000 −5.770 [110]−0.385 −2.43 0.62 (HM) 0.123 (VB) YXZXYXZXBACA 5.60 1.0012 11.000 −5.091[112] −0.370 −2.29 0.60 (HM) 0.080 (VB) Co₂MnAl—Fe₂MnAl BACABACAYXZX5.69 1.0201 10.022   1.602 [112] −0.292 −0.36 0.45 0.085 (CB)BACABAZXYXZX 5.69 1.0183 9.000   1.230 [110] −0.262 −0.35 0.39 (NHM)0.017 (CB) YXZXYXZXBACA 5.68 1.0180 8.005   1.011 [110] −0.234 −0.300.42 0.055 (CB) Co₂MnAl—Co₂FeSi BACABACAYXZX 5.68 1.0155 14.000 −0.221[110] −0.390 −1.24 0.43 (HM) 0.068 (VB) BACABAZXYXZX 5.66 1.0116 15.000−1.011 [112] −0.407 −1.48 0.42 (HM) 0.187 (CB) YXZXYXZXBACA 5.66 1.012315.880 −1.160 [110] −0.390 −1.57 0.25 0.161 (VB) YXZXYXCABACA 5.681.0165 15.000 −2.206 [110] −0.382 −1.71 0.24 (HM) 0.086 (CB)Co₂MnAl—Fe₂MnGa BACABACAYXZX 5.70 1.0218 10.060   3.060 [110] −0.2550.07 0.35 0.148 (CB) BACABAZXYXZX 5.71 1.0212 9.015   1.800 [112] −0.186−0.15 0.20 0.145 (CB) YXZXYXZXBACA 5.70 1.0213 8.076   2.303 [112]−0.160 0.18 0.21 0.188 (CB) YXZXYXCABACA 5.70 1.0197 9.002   1.244 [110]−0.225 −0.34 0.31 0.075 (CB) Co₂MnSi—Fe₂TiSi BACABACAYXZX 5.65 1.000210.000 −0.529 [110] −0.504 −1.02 0.59 (HM) 0.244 (VB) BACABAZXYXZX 5.640.9998 9.000 −1.361 [112] −0.497 −1.22 0.59 (HM) 0.161 (VB) YXZXYXZXBACA5.67 1.0037 5.000 −2.456 [110] −0.585 −1.87 0.48 (HM) 0.169 (VB)YXZXYXCABACA 5.68 1.0057 6.000 −2.487 [112] −0.594 −1.74 0.52 (HM) 0.124(VB) Co₂MnSi—Co₂FeSi BACABACAYXZX 5.63 0.9994 15.998 −0.301 [112] −0.418−1.44 0.46 (NHM) 0.013 (VB) YXZXYXZX-BACA 5.63 0.9987 16.401 −0.206[112] −0.388 −1.46 0.24 0.357 (VB) CoMnP—CoTiP BOCABOCAYOZX 5.39 0.95226.000   3.784 [112] −0.452 1.00 1.39 (HM) 0.693 (CB) YOZXYOCABOCA 5.420.9578 3.000   5.019 [110] −0.624 4.01 1.39 (HM) 0.576 (CB)Co₂MnSi—CoTiSi BACABACAYOZX 5.60 0.9999 9.000   5.108 [112] −0.506 0.810.73 (HM) 0.361 (CB) YOZXYOZXBACA 5.57 0.9905 3.000   5.457 [112] −0.6074.78 0.56 (HM) 0.023 (VB)

The magnetic anisotropy of a layered Heusler system (e.g., a Heuslersuperlattice) can stem from two factors: (1) the difference in theelectronic system between the two Heuslers in the superlattice and (2)lattice distortion. Most of the Heusler superlattices discussed hereinhave a relatively small stretching or contraction in the stackingdirection compared to the in-plane direction. Moreover, no strong orobvious correlation between the anisotropy and the lattice distortionwas observed. These observations suggest that the induced magneticanisotropy can be due to the difference in the electronic structure ofthe two Heusler constituents.

In order to test the hypothesis that the contrast in electronicstructure can be more important for anisotropy than the changes inatomic positions, the electronic structure of two systems wasrecalculated for the ideal layered structure and compared the to theresult for the relaxed layered structure. For Co₂MnAl—Fe₂MnGa, theeffect of the distortion was small. The undistorted calculation islisted in Table 2 as the row with c/a=1.0000. On the other hand, forCo₂MnSi—CoTiSi, the relaxation seemed to be important both for theanisotropy and for the existence of the gap.

As discussed above, for some superlattices, even though the system hasperpendicular anisotropy, the perpendicular anisotropy field is notstrong enough to overcome the demagnetization field of a thin film(e.g., Co₂MnAl—Fe₂MnAl with n=1.5 layering and [001] stacking,Co₂MnAl—Fe₂MnGa with n=1.0 or 1.5 layering and [110] stacking).

The calculated magnetic anisotropy for the sixteen [001]-layered Heusleralloys is shown in Table 2. For each system, the anisotropy wascalculated for n=0.5, 1.0 and 1.5. Sixteen of these 48 systems werefound to have perpendicular anisotropy. Of these 16 with perpendicularanisotropy, 7 were found to have sufficient perpendicular anisotropy toexceed the thin film demagnetization field.

Co₂MnAl—Fe₂MnAl with n=0.5 is predicted to be a near half-metal withperpendicular magnetic anisotropy; the density of states for thislayered system is shown in FIG. 5A. Co₂TiGe—Fe₂TiGe with n=1.0 ispredicted to be a half-metal with perpendicular magnetic anisotropy; thedensity of states for this layered system is shown in FIG. 5B.CoMnP—CoTiP with n=0.5 is a layered combination of half-Heuslers thatcombines a relatively strong perpendicular anisotropy with wide band-gaphalf-metallicity. Interestingly, both Fe₂TiGe and CoTiP areSlater-Pauling semiconductors.

For [110] layering, the same 16 Heusler combinations as for [001]layering were investigated. For some of the n=0.5 thickness systems with[110] layering, the [110] direction is equivalent to the [110]direction. These systems cannot have perpendicular anisotropy in the[110] direction. This consideration reduces the number of systems to 39compared to 48 for the [001] direction. Thirteen of the 39 [110] systemswere found to have perpendicular magnetocrystalline anisotropy. Of the13 with perpendicular magnetocrystalline anisotropy, 5 had sufficientperpendicular magnetic anisotropy to be perpendicular as a thin film. Ofthese 5 predicted to be perpendicular as a thin film, 3 were also halfmetals. The full-Heusler-half-Heusler combination, Co₂MnSi—CoTiSi withn=1 is predicted to have perpendicular magnetic anisotropy and to be ahalf-metal with a relatively large band gap. The density of states forthis superlattice is shown in FIG. 6A.

For [111] layering we investigated 8 pairs of Heuslers. Even for aminimal 12 atomic layer supercell (9 atomic layers if both arehalf-Heuslers) there are several ways the layers can be arranged whilestill maintaining the local Heusler environment. In all we investigated24 [111] layered systems. Of these 24, 11 were calculated to haveperpendicular magnetic anisotropy and of the 11 with perpendicularmagnetic anisotropy we calculated that 6 would be perpendicular as thinfilms. The sign of the magnetocrystalline anisotropy was consistent forall of the [111] layer schemes that we tried for a given pair ofHeuslers. The [111] layered half-Heusler system CoMnP—CoTiP is predictedto be half metallic as well as perpendicular with a large band gap. Thedensity of states for this superlattice is shown in FIG. 6B.

For some applications of half-metals, it can be desirable to have theFermi energy fall near the center of the gap of the gapped spin-channel.Many of the half-metallic Heusler superlattices with perpendicularanisotropy investigated herein have a Fermi level close to the valenceband edge (e.g., [001] direction stacked, n=0.5 superlattice ofCo₂MnAl—Fe₂MnAl). The position of the Fermi level and the gap width canbe engineered by doping the superlattice with atoms with a higher orlower count of valence electrons (Balke B et al. Phys. Rev. B. 2006, 74,104405; Miura Y et al. Phys. Rev. B. 2004, 69, 144413; Antonov V N etal. Phys. Rev. B. 2005, 72, 054441).

In order to move the Fermi level away from the valence band edge towardthe band gap in the [001] direction stacked n=0.5 superlattice ofCo₂MnAl—Fe₂MnAl, the alloy was doped with Si atoms at the Al atom sitesor with Cr atoms at the Mn sites to add electrons and thereby move theFermi energy up relative to the gap. FIG. 7A shows the density of statesof the [001] direction stacked superlattice of Co₂MnAl—Fe₂MnAl with Sidoping. For cases (i) and (ii), the Al and Si atoms were not mixed in a(001) plane. For case (i) one in every four Mn—Al atomic planes werereplaced with Mn—Si planes ( . . . —Co₂—MnAl—Fe₂—MnAl—Co₂—MnAl—Fe₂—MnSi—. . . ). In case (ii), two of the Mn—Al planes were replaced with Mn—Si( . . . —Co₂—MnAl—Fe₂—MnAl—Co₂—MnAl—Fe₂—MnSi— . . . ). For cases (iii)and (iv), both Al and Si atoms can be in a (001) plane.

For Co₂MnAl—Fe₂MnAl, the Fermi Level is 0.015 eV inside the valenceband. In all cases of doping, addition of Si atoms shifted the Fermilevel into the band gap. When 50% of the Al atoms were replaced with Siatoms (cases (ii) and (iv)), the Fermi level moved 0.05 eV into the bandgap relative to the valence band edge. For 25% doping, the Fermi levelmoved 0.03 eV into the band gap. The improvement in half-metallicitycame at the cost of the perpendicular anisotropy. For 25% Si doping atthe Al sites, the anisotropy dropped from 6.08×10⁵ J/m³ to 5.02×10⁵ J/m³and 4.8×10⁵ J/m³ for cases (i) and (iii), respectively. For 40% Sidoping, the anisotropy dropped to 2.16×10⁵ J/m³ and 1.08×10⁵ J/m³ forcases (ii) and (iv), respectively.

FIG. 7B shows the effect of Fe or Cr doping at the Mn atom sites.Addition of Fe atoms moved the Fermi level 0.043 eV into the valenceband. Addition of Cr atoms placed the Fermi level in the middle of theband gap. However, the bandgap was reduced to 0.1 eV and the anisotropydropped to 1.47×10⁵ J/m³.

One drawback of half-metallic Heusler alloys for application asferromagnetic layers in certain spintronic devices is that they do nothave uniaxial magnetocrystalline anisotropy. To address these and otherissues, layered Heusler alloys were investigated by studyingsuperlattices stacked in the [001], [110], or [111] directions fordifferent thickness. The results indicate that two Heusler alloysstacked in the [001], [110], or [111] directions for various thicknessesto form a superlattice, can still satisfy the Slater-Pauling rule andthe resulting superlattice can be half-metallic with gaps comparable toor larger than those of its constituents. The Slater-Pauling gapscharacteristics of many L2₁ (full) and C1_(b) (half) Heusler alloys werefound to be robust in the presence of layering in the [001], [110], or[111] directions. This was found for L2₁-L2₁, L2₁-C1_(b), andC1_(b)-C1_(b) combinations. The results discussed herein also predictedthat it is possible to achieve uniaxial anisotropy by layering twoHeusler alloys and that said uniaxial magnetocrystalline anisotropy canbe due to the differences in the electronic structure of the twoHeuslers in the superlattice.

Other advantages which are obvious and which are inherent to theinvention will be evident to one skilled in the art. It will beunderstood that certain features and sub-combinations are of utility andmay be employed without reference to other features andsub-combinations. This is contemplated by and is within the scope of theclaims. Since many possible examples may be made of the inventionwithout departing from the scope thereof, it is to be understood thatall matter herein set forth or shown in the accompanying drawings is tobe interpreted as illustrative and not in a limiting sense.

What is claimed is:
 1. A layered Heusler alloy, comprising: a firstlayer comprising a first Heusler alloy with a face-centered cubic (fcc)crystal structure; a second layer comprising a second Heusler alloy witha fcc crystal structure, the second Heusler alloy being different thanthe first Heusler alloy; wherein the first layer and the second layerare layered along a layering direction, the layering direction being the[110] or [111] direction of the fcc crystal structure, thereby formingthe layered Heusler alloy; wherein the layered Heusler alloy has amagnetocrystalline anisotropy of greater than 0 J/m³ along a directionperpendicular to the layering direction; wherein the layered Heusleralloy comprises a half metal or a near half metal; and wherein thelayered Heusler alloy has a Fermi level and a gapped spin-channel with agap, and wherein the Fermi level of the layered Heusler alloy fallswithin the gap of the gapped spin-channel of the layered Heusler alloy.2. The layered Heusler alloy of claim 1, wherein: the layered Heusleralloy is layered along the [110] direction; the first Heusler alloy hasa formula A_(p)BC, wherein: p is 1 or 2; A and B are each a transitionmetal, with the proviso that A and B are not the same transition metal;and C is an element from Group 13, 14, or 15; the first layer comprisesa first number of sublayers; the second Heusler alloy has a formulaX_(q)YZ, wherein: q is 1 or 2; X and Y are each a transition metal, withthe proviso that X and Y are not the same transition metal; and Z is anelement from Group 13, 14, or 15; the second layer comprises a secondnumber of sublayers; and the first number of sublayers is the same asthe second number of sublayers, such that the layered Heusler alloy hasa unit cell comprising (A_(p)BC)a(X_(q)YZ)a, wherein a is the firstnumber of sublayers and a is an integer from 1 to
 1000. 3. The layeredHeusler alloy of claim 2, wherein: A and B are selected from the groupconsisting of: scandium, titanium, vanadium, chromium, manganese, iron,cobalt, nickel, yttrium, zirconium, niobium, molybdenum, technetium,ruthenium, rhodium, and palladium; and X and Y are selected from thegroup consisting of: scandium, titanium, vanadium, chromium, manganese,iron, cobalt, nickel, yttrium, zirconium, niobium, molybdenum,technetium, ruthenium, rhodium, and palladium.
 4. The layered Heusleralloy of claim 2, wherein: A and B are selected from the groupconsisting of: titanium, vanadium, chromium, manganese, iron, cobalt,nickel, rhodium, and palladium; and X and Y are selected from the groupconsisting of: titanium, vanadium, chromium, manganese, iron, cobalt,nickel, rhodium, and palladium.
 5. The layered Heusler alloy of claim 2,wherein C and Z are independently selected from the group consisting of:boron, aluminum, gallium, indium, thallium, carbon, silicon, germanium,tin, lead, nitrogen, phosphorous, arsenic, antimony, and bismuth.
 6. Thelayered Heusler alloy of claim 2, wherein C and Z are independentlyselected from the group consisting of: aluminum, gallium, silicon,germanium, tin, phosphorous, arsenic, and antimony.
 7. The layeredHeusler alloy of claim 1, wherein the layered Heusler alloy is layeredalong the [111] direction; the first Heusler alloy has a formulaA_(p)BC, wherein: p is 1 or 2; A and B are each a transition metal, withthe proviso that A and B are not the same transition metal; and C is anelement from Group 13, 14, or 15; the first layer comprises a firstnumber of sublayers, the first number of sublayers being 4, 6, or 8; thesecond Heusler alloy has a formula X_(q)YZ, wherein: q is 1 or 2; X andY are each a transition metal, with the proviso that X and Y are not thesame transition metal; and Z is an element from Group 13, 14, or 15; thesecond layer comprises a second number of sublayers, the second numberof sublayers being 4, 6, or 8; and the sum of the first number ofsublayers and second number of sublayers is 12, such that: when thefirst number of sublayers is 4, the layered Heusler alloy has a unitcell comprising (A_(p)BC)(X_(q)YZ)₂, wherein p and q are independently 1or 2; when the first number of sublayers is 8, the layered Heusler alloyhas a unit cell comprising (A_(p)BC)₂(X_(q)YZ), wherein p and q areindependently 1 or 2; and when the first number of sublayers is 6, thelayered Heusler alloy has a unit cell comprising(A_(p)BC)(A_(p-1)XBZ)(X_(q)YZ), wherein p and q are independently 1 or2.
 8. The layered Heusler alloy of claim 7, wherein: A and B areselected from the group consisting of: scandium, titanium, vanadium,chromium, manganese, iron, cobalt, nickel, yttrium, zirconium, niobium,molybdenum, technetium, ruthenium, rhodium, and palladium; and X and Yare selected from the group consisting of: scandium, titanium, vanadium,chromium, manganese, iron, cobalt, nickel, yttrium, zirconium, niobium,molybdenum, technetium, ruthenium, rhodium, and palladium.
 9. Thelayered Heusler alloy of claim 7, wherein: A and B are selected from thegroup consisting of: titanium, vanadium, chromium, manganese, iron,cobalt, nickel, rhodium, and palladium; and X and Y are selected fromthe group consisting of: titanium, vanadium, chromium, manganese, iron,cobalt, nickel, rhodium, and palladium.
 10. The layered Heusler alloy ofclaim 7, wherein C and Z are independently selected from the groupconsisting of: boron, aluminum, gallium, indium, thallium, carbon,silicon, germanium, tin, lead, nitrogen, phosphorous, arsenic, antimony,and bismuth.
 11. The layered Heusler alloy of claim 7, wherein C and Zare independently selected from the group consisting of: aluminum,gallium, silicon, germanium, tin, phosphorous, arsenic, and antimony.12. The layered Heusler alloy of claim 1, wherein the first Heusleralloy and the second Heusler alloy are selected from the groupconsisting of Co₂CrSi, Co₂CrSb, Co₂FeSi, Co₂MnAl, Co₂MnSi, Co₂MnSb,Co₂TiGe, Co₂VGa, Co₂VSn, Fe₂MnAl, Fe₂MnGa, Fe₂MnSi, Fe₂TiGe, Fe₂TiSi,CoMnP, CoTiP, RhFeGe, RuMnAs, NiMnP, NiMnSi, NiMnAs, NiMnSb, NiVSb,CoMnSb, and CoTiSi.
 13. The layered Heusler alloy of claim 1, whereinthe first Heusler alloy comprises a half metal or a near half metal. 14.The layered Heusler alloy of claim 1, wherein the second Heusler alloycomprises a half metal or a near half metal.
 15. The layered Heusleralloy of claim 1, wherein the magnetocrystalline anisotropy of thelayered Heusler alloy along a direction perpendicular to the layeringdirection is from greater than 0 J/m³ to 10⁶ J/m³.
 16. The layeredHeusler alloy of claim 1, wherein the μ₀H_(eff) of the layered Heusleralloy is from −10 to 10¹⁰ N A⁻¹ m⁻¹.
 17. The layered Heusler alloy ofclaim 1, wherein the layered Heusler alloy has a μ₀H_(eff) of greaterthan 0 N A⁻¹ m⁻¹.
 18. The layered Heusler alloy of claim 1, wherein thelayered Heusler alloy further comprises: a third layer comprising athird Heusler alloy with a fcc crystal structure, the third Heusleralloy being different than the first Heusler alloy, the second Heusleralloy, or combinations thereof; and the first layer, the second layer,and the third layer are layered along the layering direction.